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Journal articles on the topic 'Deviation estimates'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Korolyuk, V. S., and O. Melyaeva. "Martingale estimates for the distribution of the deviation of density estimates." Ukrainian Mathematical Journal 38, no. 1 (1986): 94–97. http://dx.doi.org/10.1007/bf01056768.

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2

Buraczewski, Dariusz, and Mariusz Maślanka. "Large deviation estimates for branching random walks." ESAIM: Probability and Statistics 23 (2019): 823–40. http://dx.doi.org/10.1051/ps/2019006.

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3

Naudts, Jan, and Hiroki Suyari. "Large deviation estimates involving deformed exponential functions." Physica A: Statistical Mechanics and its Applications 436 (October 2015): 716–28. http://dx.doi.org/10.1016/j.physa.2015.05.093.

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4

Pechenin, Vadim Andreevich, Michael Alexandrovich Bolotov, and N. V. Ruzanov. "Technique of Decomposition of Form Deviation for Freeform Surfaces." Key Engineering Materials 685 (February 2016): 334–39. http://dx.doi.org/10.4028/www.scientific.net/kem.685.334.

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This paper presents the technique of decomposition of form deviation based on the use of wavelet filter and Fourier transform. The method allows decomposing the total deviation into systematic, random systematic (waviness) and random components. The method testing was carried out for the statistics of the deviation of the suction side of the turbine engine compressor blade. The accuracy check of the estimates of form deviations generated by the method in a series of simulated surfaces with pre-laid characteristics was carried out. The results showed that the method of decomposition allows one to estimate exactly the components of the form deviation of the simulated surfaces in their series.

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5

Uzhga Rebrov, Oleg, and Galina Kuleshova. "FUZZY ROBUST ESTIMATES OF LOCATION AND SCALE PARAMETERS OF A FUZZY RANDOM VARIABLE." ENVIRONMENT. TECHNOLOGIES. RESOURCES. Proceedings of the International Scientific and Practical Conference 2 (June 17, 2021): 181–86. http://dx.doi.org/10.17770/etr2021vol2.6566.

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A random variable is a variable whose components are random values. To characterise a random variable, the arithmetic mean is widely used as an estimate of the location parameter, and variation as an estimate of the scale parameter. The disadvantage of the arithmetic mean is that it is sensitive to extreme values, outliers in the data. Due to that, to characterise random variables, robust estimates of the location and scale parameters are widely used: the median and median absolute deviation from the median. In real situations, the components of a random variable cannot always be estimated in a deterministic way. One way to model the initial data uncertainty is to use fuzzy estimates of the components of a random variable. Such variables are called fuzzy random variables. In this paper, we examine fuzzy robust estimates of location and scale parameters of a fuzzy random variable: fuzzy median and fuzzy median of the deviations of fuzzy component values from the fuzzy median.

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6

Shulenin, V. P. "Comparison of robust estimates of modified variants of standard deviation and average absolute deviations." Izvestiya vysshikh uchebnykh zavedenii. Fizika 65, no. 2 (February 1, 2022): 171–80. http://dx.doi.org/10.17223/00213411/65/2/171.

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7

Goddard, M. J. "Tables to calculate untrimmed range and standard deviation estimates from trimmed estimates." Communications in Statistics - Simulation and Computation 23, no. 1 (January 1994): 207–21. http://dx.doi.org/10.1080/03610919408813165.

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8

Doukhan, Paul, and Elisabeth Gassiat. "Quadratic deviation of penalized mean squares regression estimates." Journal of Multivariate Analysis 41, no. 1 (April 1992): 89–101. http://dx.doi.org/10.1016/0047-259x(92)90059-o.

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9

Sakhanenko, A. I. "Berry-esseen type estimates for large deviation probabilities." Siberian Mathematical Journal 32, no. 4 (1992): 647–56. http://dx.doi.org/10.1007/bf00972983.

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10

Mrode, R. A., C. Smith, and R. Thompson. "Selection for rate and efficiency of lean gain in Hereford cattle 1. Selection pressure applied and direct responses." Animal Science 51, no. 1 (August 1990): 23–34. http://dx.doi.org/10.1017/s0003356100005122.

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ABSTRACTSelection of bulls for rate and efficiency of lean gain was studied in a herd of Hereford cattle. There were two selection lines, one selected for lean growth rate (LGR) from birth to 400 days and the other for lean food conversion ratio (LFCR) from 200 to 400 days of age, for a period of 8 years. A control line bred by frozen semen from foundation bulls was also maintained. Generation interval was about 2·4 years and average male selection differentials, per generation were 1·2 and — 1·1 phenotypic standard deviation units for LGR and LFCR respectively.Genetic parameters and responses to selection were estimated from the deviation of the selected lines from a control line and by restricted maximum likelihood (REML) techniques on the same material. Realized heritabilities were 0·40 (s.e. 0·12) for LGR and 0·40 (s.e. 0·13) for LFCR using the control line. Corresponding estimates from REML were 0·42 (s.e. 0·10) and 0·37 (s.e. 0·14). The estimate of the genetic correlation between LGR and LFCR was about — 0·69 (s.e. 0·12) using REML.The estimates of direct annual genetic change using deviations from the control were 3·6 (s.e. 1·3) g/day for LGR and — 0·14 (s.e. 0·07) kg food per kg lean gain for LFCR. Corrsponding estimates from REML were similar but more precisely estimated. The correlated responses for LFCR in the LGR line was higher than the direct response for LFCR.

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11

Shulenin, Valery P. "Asymptotic properties and robustness of trimmed versions estimates of standard deviation and mean absolute deviations." Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitel'naya tekhnika i informatika, no. 55 (June 1, 2021): 91–102. http://dx.doi.org/10.17223/19988605/55/11.

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12

Ang, James S., Gwoduan David Jou, and Tsong-Yue Lai. "Alternative Formulas to Compute Implied Standard Deviation." Review of Pacific Basin Financial Markets and Policies 12, no. 02 (June 2009): 159–76. http://dx.doi.org/10.1142/s0219091509001599.

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We assume that the call option's value is correctly priced by Black and Scholes' option pricing model in this paper. This paper derives an exact closed-form solution for implied standard deviation under the condition that the underlying asset price equals the present value of the exercise price. The exact closed-form solution provides the true implied standard deviation and has no estimate error. This paper also develops three alternative formulas to estimate the implied standard deviation if this condition is violated. Application of the Taylor expansion on a single call option value derives the first formula. The accuracy of this formula depends on the deviation between the underlying asset price and the present value of the exercise price. Use of the Taylor formula on two call option prices with different exercise prices is used to develop the second formula, which can be used even though the underlying asset price deviates significantly from the present value of the exercise price. Extension of the second formula's approach to third options value derives the third formula. A merit of the third formula is to circumvent a required parameter used in the second formula. Simulations demonstrate that the implied standard deviations calculated by the second and third formulas provide accurate estimates of the true implied standard deviations.

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13

Cigagna, Cristiano, Daniel Marcos Bonotto, José Ricardo Sturaro, and Antonio Fernando Monteiro Camargo. "Geostatistical techniques applied to mapping limnological variables and quantify the uncertainty associated with estimates." Acta Limnologica Brasiliensia 27, no. 4 (December 2015): 421–30. http://dx.doi.org/10.1590/s2179-975x3315.

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Abstract Aim: This study aimed to map the concentrations of limnological variables in a reservoir employing semivariogram geostatistical techniques and Kriging estimates for unsampled locations, as well as the uncertainty calculation associated with the estimates. Methods: We established twenty-seven points distributed in a regular mesh for sampling. Then it was determined the concentrations of chlorophyll-a, total nitrogen and total phosphorus. Subsequently, a spatial variability analysis was performed and the semivariogram function was modeled for all variables and the variographic mathematical models were established. The main geostatistical estimation technique was the ordinary Kriging. The work was developed with the estimate of a heavy grid points for each variables that formed the basis of the interpolated maps. Results: Through the semivariogram analysis was possible to identify the random component as not significant for the estimation process of chlorophyll-a, and as significant for total nitrogen and total phosphorus. Geostatistical maps were produced from the Kriging for each variable and the respective standard deviations of the estimates calculated. These measurements allowed us to map the concentrations of limnological variables throughout the reservoir. The calculation of standard deviations provided the quality of the estimates and, consequently, the reliability of the final product. Conclusions: The use of the Kriging statistical technique to estimate heavy mesh points associated with the error dispersion (standard deviation of the estimate), made it possible to make quality and reliable maps of the estimated variables. Concentrations of limnological variables in general were higher in the lacustrine zone and decreased towards the riverine zone. The chlorophyll-a and total nitrogen correlated comparing the grid generated by Kriging. Although the use of Kriging is more laborious compared to other interpolation methods, this technique is distinguished for its ability to minimize the variance of the estimate and provide the estimated value of the degree of uncertainty.

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14

McConachie, Sean M., Claudia M. Hanni, Joshua N. Raub, Rima A. Mohammad, and Sheila M. Wilhelm. "The Impact of Multiple Renal Estimates on Pharmacist Dosing Recommendations: A Randomized Trial." Annals of Pharmacotherapy 55, no. 1 (June 24, 2020): 25–35. http://dx.doi.org/10.1177/1060028020935447.

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Background: Numerous equations are used for estimation of renal function, and many electronic medical records report multiple clearance estimates to assist with drug dosing. It is unknown whether the presence of multiple clearance estimates affects clinical decision-making. Objective: To determine whether the presence of multiple renal clearance estimates affects pharmacist drug dosing decisions. Methods: A randomized trial in the form of an electronic survey including 4 clinical vignettes was delivered to hospital pharmacists. Vignettes consisted of a patient presenting with an acute pulmonary embolism requiring enoxaparin therapy. Pharmacists were randomized to receive a single estimate of renal function or multiple estimates for all vignettes. The primary outcome was deviation from approved recommendations on at least 1 vignette. The χ2 test was used to detect differences in deviation rates between groups. Logistic regression was performed to adjust for the effects of potentially confounding variables. Results: A total of 154 studies were completed (73 in the multiple-estimate group and 81 in the single-estimate group). Pharmacists presented with multiple renal estimates were significantly more likely to deviate from recommended dosing regimens than pharmacists presented with a single estimate (54.7% vs 38.2%; P = 0.04). The results were driven primarily by the 2 vignettes that included discordance among Cockcroft-Gault equation creatinine clearance estimates. Logistic regression identified multiple estimates as the only independent predictor of deviation ( P = 0.04). Conclusion and Relevance: Pharmacists provided with a single renal clearance estimate were more likely to adhere to approved dosing recommendations than pharmacists provided with multiple estimates.

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15

Henrique, Douglas Sampaio, Ricardo Augusto Mendonça Vieira, Pedro Antônio Muniz Malafaia, Maurício Cordeiro Mancini, and André Luigi Gonçalves. "Estimation of the total efficiency of metabolizable energy utilization for maintenance and growth by cattle in tropical conditions." Revista Brasileira de Zootecnia 34, no. 3 (June 2005): 1006–16. http://dx.doi.org/10.1590/s1516-35982005000300034.

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Data of 320 animals were obtained from eight comparative slaughter studies performed under tropical conditions and used to estimate the total efficiency of utilization of the metabolizable energy intake (MEI), which varied from 77 to 419 kcal kg-0.75d-1. The provided data also contained direct measures of the recovered energy (RE), which allowed calculating the heat production (HE) by difference. The RE was regressed on MEI and deviations from linearity were evaluated by using the F-test. The respective estimates of the fasting heat production and the intercept and the slope that composes the relationship between RE and MEI were 73 kcal kg-0.75d-1, 42 kcal kg-0.75d-1 and 0.37. Hence, the total efficiency was estimated by dividing the net energy for maintenance and growth by the metabolizable energy intake. The estimated total efficiency of the ME utilization and analogous estimates based on the beef cattle NRC model were employed in an additional study to evaluate their predictive powers in terms of the mean square deviations for both temperate and tropical conditions. The two approaches presented similar predictive powers but the proposed one had a 22% lower mean squared deviation even with its more simplified structure.

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16

Lasslop, G., M. Reichstein, J. Kattge, and D. Papale. "Influences of observation errors in eddy flux data on inverse model parameter estimation." Biogeosciences Discussions 5, no. 1 (February 14, 2008): 751–85. http://dx.doi.org/10.5194/bgd-5-751-2008.

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Abstract. Eddy covariance data are increasingly used to estimate parameters of ecosystem models and for proper maximum likelihood parameter estimates the error structure in the observed data has to be fully characterized. In this study we propose a method to characterize the random error of the eddy covariance flux data, and analyse error distribution, standard deviation, cross- and autocorrelation of CO2 and H2O flux errors at four different European eddy covariance flux sites. Moreover, we examine how the treatment of those errors and additional systematic errors influence statistical estimates of parameters and their associated uncertainties with three models of increasing complexity – a hyperbolic light response curve, a light response curve coupled to water fluxes and the SVAT scheme BETHY. In agreement with previous studies we find that the error standard deviation scales with the flux magnitude. The previously found strongly leptokurtic error distribution is revealed to be largely due to a superposition of almost Gaussian distributions with standard deviations varying by flux magnitude. The crosscorrelations of CO2 and H2O fluxes were in all cases negligible (R2 below 0.2), while the autocorrelation is usually below 0.6 at a lag of 0.5 hours and decays rapidly at larger time lags. This implies that in these cases the weighted least squares criterion yields maximum likelihood estimates. To study the influence of the observation errors on model parameter estimates we used synthetic datasets, based on observations of two different sites. We first fitted the respective models to observations and then added the random error estimates described above and the systematic error, respectively, to the model output. This strategy enables us to compare the estimated parameters with true parameters. We show that the correct implementation of the random error standard deviation scaling with flux magnitude significantly reduces the parameter uncertainty and often yields parameter retrievals that are closer to the true value, than by using ordinary least squares. The systematic error leads to systematically biased parameter estimates, but its impact varies by parameter. The parameter uncertainty slightly increases, but the true parameter is not within the uncertainty range of the estimate. This means that the uncertainty is underestimated with current approaches that neglect selective systematic errors in flux data. Hence, we conclude that potential systematic errors in flux data need to be addressed more thoroughly in data assimilation approaches since otherwise uncertainties will be vastly underestimated.

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17

Lasslop, G., M. Reichstein, J. Kattge, and D. Papale. "Influences of observation errors in eddy flux data on inverse model parameter estimation." Biogeosciences 5, no. 5 (September 17, 2008): 1311–24. http://dx.doi.org/10.5194/bg-5-1311-2008.

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Abstract. Eddy covariance data are increasingly used to estimate parameters of ecosystem models. For proper maximum likelihood parameter estimates the error structure in the observed data has to be fully characterized. In this study we propose a method to characterize the random error of the eddy covariance flux data, and analyse error distribution, standard deviation, cross- and autocorrelation of CO2 and H2O flux errors at four different European eddy covariance flux sites. Moreover, we examine how the treatment of those errors and additional systematic errors influence statistical estimates of parameters and their associated uncertainties with three models of increasing complexity – a hyperbolic light response curve, a light response curve coupled to water fluxes and the SVAT scheme BETHY. In agreement with previous studies we find that the error standard deviation scales with the flux magnitude. The previously found strongly leptokurtic error distribution is revealed to be largely due to a superposition of almost Gaussian distributions with standard deviations varying by flux magnitude. The crosscorrelations of CO2 and H2O fluxes were in all cases negligible (R2 below 0.2), while the autocorrelation is usually below 0.6 at a lag of 0.5 h and decays rapidly at larger time lags. This implies that in these cases the weighted least squares criterion yields maximum likelihood estimates. To study the influence of the observation errors on model parameter estimates we used synthetic datasets, based on observations of two different sites. We first fitted the respective models to observations and then added the random error estimates described above and the systematic error, respectively, to the model output. This strategy enables us to compare the estimated parameters with true parameters. We illustrate that the correct implementation of the random error standard deviation scaling with flux magnitude significantly reduces the parameter uncertainty and often yields parameter retrievals that are closer to the true value, than by using ordinary least squares. The systematic error leads to systematically biased parameter estimates, but its impact varies by parameter. The parameter uncertainty slightly increases, but the true parameter is not within the uncertainty range of the estimate. This means that the uncertainty is underestimated with current approaches that neglect selective systematic errors in flux data. Hence, we conclude that potential systematic errors in flux data need to be addressed more thoroughly in data assimilation approaches since otherwise uncertainties will be vastly underestimated.

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18

Duarte, Pedro, and Silvius Klein. "Large deviation type estimates for iterates of linear cocycles." Stochastics and Dynamics 16, no. 03 (March 8, 2016): 1660010. http://dx.doi.org/10.1142/s0219493716600108.

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We describe some methods used to derive large deviation type (LDT) estimates for quantities associated to random and quasi-periodic linear cocycles. We then explain how such LDT estimates can be used in an inductive scheme to prove continuity properties of the Lyapunov exponents as functions of the cocycle. This is a survey of recent work to appear in a research monograph.

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19

Ganesan, Ghurumuruhan. "Deviation estimates for Eulerian edit numbers of random graphs." Statistics & Probability Letters 171 (April 2021): 109025. http://dx.doi.org/10.1016/j.spl.2020.109025.

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20

Frehlich, Rod, and Larry Cornman. "Estimating Spatial Velocity Statistics with Coherent Doppler Lidar." Journal of Atmospheric and Oceanic Technology 19, no. 3 (March 1, 2002): 355–66. http://dx.doi.org/10.1175/1520-0426-19.3.355.

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Abstract The spatial statistics of a simulated turbulent velocity field are estimated using radial velocity estimates from simulated coherent Doppler lidar data. The structure functions from the radial velocity estimates are processed to estimate the energy dissipation rate ε and the integral length scale Li, assuming a theoretical model for isotropic wind fields. The performance of the estimates are described by their bias, standard deviation, and percentiles. The estimates of ε2/3 are generally unbiased and robust. The distribution of the estimates of Li are highly skewed; however, the median of the distribution is generally unbiased. The effects of the spatial averaging by the atmospheric movement transverse to the lidar beam during the dwell time of each radial velocity estimate are determined, as well as the error scaling as a function of the dimensions of the total measurement region. Accurate estimates of Li require very large measurement domains in order to observe a large number of independent samples of the spatial scales that define Li.

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21

Curran-Everett, Douglas. "Explorations in statistics: standard deviations and standard errors." Advances in Physiology Education 32, no. 3 (September 2008): 203–8. http://dx.doi.org/10.1152/advan.90123.2008.

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Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This series in Advances in Physiology Education provides an opportunity to do just that: we will investigate basic concepts in statistics using the free software package R. Because this series uses R solely as a vehicle with which to explore basic concepts in statistics, I provide the requisite R commands. In this inaugural paper we explore the essential distinction between standard deviation and standard error: a standard deviation estimates the variability among sample observations whereas a standard error of the mean estimates the variability among theoretical sample means. If we fail to report the standard deviation, then we fail to fully report our data. Because it incorporates information about sample size, the standard error of the mean is a misguided estimate of variability among observations. Instead, the standard error of the mean provides an estimate of the uncertainty of the true value of the population mean.

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22

Eddy, Tyler D., William W. L. Cheung, and John F. Bruno. "Historical baselines of coral cover on tropical reefs as estimated by expert opinion." PeerJ 6 (January 24, 2018): e4308. http://dx.doi.org/10.7717/peerj.4308.

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Coral reefs are important habitats that represent global marine biodiversity hotspots and provide important benefits to people in many tropical regions. However, coral reefs are becoming increasingly threatened by climate change, overfishing, habitat destruction, and pollution. Historical baselines of coral cover are important to understand how much coral cover has been lost, e.g., to avoid the ‘shifting baseline syndrome’. There are few quantitative observations of coral reef cover prior to the industrial revolution, and therefore baselines of coral reef cover are difficult to estimate. Here, we use expert and ocean-user opinion surveys to estimate baselines of global coral reef cover. The overall mean estimated baseline coral cover was 59% (±19% standard deviation), compared to an average of 58% (±18% standard deviation) estimated by professional scientists. We did not find evidence of the shifting baseline syndrome, whereby respondents who first observed coral reefs more recently report lower estimates of baseline coral cover. These estimates of historical coral reef baseline cover are important for scientists, policy makers, and managers to understand the extent to which coral reefs have become depleted and to set appropriate recovery targets.

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23

PARK, LEEYOUNG. "Effective population size of current human population." Genetics Research 93, no. 2 (March 31, 2011): 105–14. http://dx.doi.org/10.1017/s0016672310000558.

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SummaryIn order to estimate the effective population size (Ne) of the current human population, two new approaches, which were derived from previous methods, were used in this study. One is based on the deviation from linkage equilibrium (LE) between completely unlinked loci in different chromosomes and another is based on the deviation from the Hardy–Weinberg Equilibrium (HWE). When random mating in a population is assumed, genetic drifts in population naturally induce linkage disequilibrium (LD) between chromosomes and the deviation from HWE. The latter provides information on the Ne of the current population, and the former provides the same when the Ne is constant. If Ne fluctuates, recent Ne changes are reflected in the estimates based on LE, and the comparison between two estimates can provide information regarding recent changes of Ne. Using HapMap Phase III data, the estimates were varied from 622 to 10 437, depending on populations and estimates. The Ne appeared to fluctuate as it provided different estimates for each of the two methods. These Ne estimates were found to agree approximately with the overall increment observed in recent human populations.

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24

Ushakov, V. N., and M. V. Pershakov. "On estimation of Hausdorff deviation of convex polygons in $\mathbb{R}^2$ from their differences with disks." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 30, no. 4 (December 2020): 585–603. http://dx.doi.org/10.35634/vm200404.

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We study a problem concerning the estimation of the Hausdorff deviation of convex polygons in $\mathbb R^2$ from their geometric difference with circles of sufficiently small radius. Problems with such a subject, in which not only convex polygons but also convex compacts in the Euclidean space $\mathbb R^n$ are considered, arise in various fields of mathematics and, in particular, in the theory of differential games, control theory, convex analysis. Estimates of Hausdorff deviations of convex compact sets in $\mathbb R^n$ in their geometric difference with closed balls in $\mathbb R^n$ are presented in the works of L.S. Pontryagin, his staff and colleagues. These estimates are very important in deriving an estimate for the mismatch of the alternating Pontryagin’s integral in linear differential games of pursuit and alternating sums. Similar estimates turn out to be useful in deriving an estimate for the mismatch of the attainability sets of nonlinear control systems in $\mathbb R^n$ and the sets approximating them. The paper considers a specific convex heptagon in $\mathbb R^2$. To study the geometry of this heptagon, we introduce the concept of a wedge in $\mathbb R^2$. On the basis of this notion, we obtain an upper bound for the Hausdorff deviation of a heptagon from its geometric difference with the disc in $\mathbb R^2$ of sufficiently small radius.

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25

Macci, Claudio, Maurizia Rossi, and Anna Paola Todino. "Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics." Latin American Journal of Probability and Mathematical Statistics 18, no. 1 (2021): FIRST PAGE. http://dx.doi.org/10.30757/alea.v18-11.

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26

Koppang, Paul A., and Christopher R. Ekstrom. "Degrees of Freedom for Allan Deviation Estimates of Multiple Clocks." IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 63, no. 4 (April 2016): 571–74. http://dx.doi.org/10.1109/tuffc.2015.2495016.

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27

Whitman, Charles S. "Impact of ambient temperature set point deviation on Arrhenius estimates." Microelectronics Reliability 52, no. 1 (January 2012): 2–8. http://dx.doi.org/10.1016/j.microrel.2011.09.023.

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28

Leonov, V. V. "Measurement comparison ina posteriori error estimates for rectilinearity deviation measurements." Measurement Techniques 37, no. 12 (December 1994): 1356–59. http://dx.doi.org/10.1007/bf00976913.

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29

Jona-Lasinio, G., and P. K. Mitter. "Large deviation estimates in the stochastic quantization ofϕ 2 4." Communications in Mathematical Physics 130, no. 1 (May 1990): 111–21. http://dx.doi.org/10.1007/bf02099877.

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30

Melo, Felipe F., and Valéria C. F. Barbosa. "Correct structural index in Euler deconvolution via base-level estimates." GEOPHYSICS 83, no. 6 (November 1, 2018): J87—J98. http://dx.doi.org/10.1190/geo2017-0774.1.

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In most applications, the Euler deconvolution aims to define the nature (type) of the geologic source (i.e., the structural index [SI]) and its depth position. However, Euler deconvolution also estimates the horizontal positions of the sources and the base level of the magnetic anomaly. To determine the correct SI, most authors take advantage of the clustering of depth estimates. We have analyzed Euler’s equation to indicate that random variables contaminating the magnetic observations and its gradients affect the base-level estimates if, and only if, the SI is not assumed correctly. Grounded on this theoretical analysis and assuming a set of tentative SIs, we have developed a new criterion for determining the correct SI by means of the minimum standard deviation of base-level estimates. We performed synthetic tests simulating multiple magnetic sources with different SIs. To produce mid and strongly interfering synthetic magnetic anomalies, we added constant and nonlinear backgrounds to the anomalies and approximated the simulated sources laterally. If the magnetic anomalies are weakly interfering, the minima standard deviations either of the depth or base-level estimates can be used to determine the correct SI. However, if the magnetic anomalies are strongly interfering, only the minimum standard deviation of the base-level estimates can determine the SI correctly. These tests also show that Euler deconvolution does not require that the magnetic data be corrected for the regional fields (e.g., International Geomagnetic Reference Field [IGRF]). Tests on real data from part of the Goiás Alkaline Province, Brazil, confirm the potential of the minimum standard deviation of base-level estimates in determining the SIs of the sources by applying Euler deconvolution either to total-field measurements or to total-field anomaly (corrected for IGRF). Our result suggests three plug intrusions giving rise to the Diorama anomaly and dipole-like sources yielding Arenópolis and Montes Claros de Goiás anomalies.

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31

Gascuel, Didier. "Une méthode simple d'ajustement des clés taille/âge : application aux captures d'albacores (Thunnus albacares) de l'Atlantique Est." Canadian Journal of Fisheries and Aquatic Sciences 51, no. 3 (March 1, 1994): 723–33. http://dx.doi.org/10.1139/f94-072.

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An adjustment method for age–length keys is presented that incorporates yearly variability in cohort abundances. The method is based on two models (one for growth and the other for standard deviations of length versus age) and involves an iterative algorithm. The algorithm rapidly converges to stable results that yield, under some conditions, maximum likelihood estimates. It is also used to estimate parameters of the length standard deviation model. The method is applied to yellowfin tuna (Thunnus albacares) catches in the eastern Atlantic from 1975 to 1989. Monthly keys, adjusted to catches from the entire fishery, show a high annual variability. These keys are used for length–age conversion by gear type and 5 geographic squares. Compared with previous estimates based on the "slicing" method, catches by age are noticeably corrected; they show a greater temporal variability. The results show a low sensitivity to parameter estimates of the length standard deviation model. The adjustment method for age–length keys is compared with classical likelihood-based methods for the separation of mixtures of normal distributions; it fits particularly well under conditions of known growth, it offers the advantages of simplicity and adaptability, and importantly, it allows the use of particular growth models.

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32

Johnson, Richard L., George W. Latimer, and Cliff Spiegelman. "Use of Trimmed Duplicates Derived from Laboratory Data To Estimate Standard Deviation." Journal of AOAC INTERNATIONAL 77, no. 6 (November 1, 1994): 1660–63. http://dx.doi.org/10.1093/jaoac/77.6.1660.

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Abstract Improved standard deviation estimates from possibly biased duplicate measurements can be derived from appropriately trimmed plots of standard deviation estimates using pairs of replicates vs the quantiles of a half-normal distribution. Simulated studies show that these estimates exhibit generally lower mean-squared errors and biases than do more standard robust estimators of location—¾ times the interquartile range and 3/2 times the mean absolute deviation from the median.

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Lamb, Robert J., Patricia A. MacKay, and Andrei Alyokhin. "Estimating population variability of aphids (Hemiptera: Aphididae): how many years are required?" Canadian Entomologist 149, no. 1 (September 14, 2016): 48–55. http://dx.doi.org/10.4039/tce.2016.34.

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AbstractVariability is an important characteristic of population dynamics, but the length of the time series required to estimate population variability is poorly understood. To this end, population variability of Macrosiphum euphorbiae (Thomas), Myzus persicae (Sulzer), and Aphis nasturtii (Kaltenbach) (Hemiptera: Aphididae) was investigated. Population variability (measured as PV, a proportion between 0 and 1) was estimated for time series of 3–62 years, giving replicate estimates for time series of 3–20 years that were normally distributed. Mean values for PV were more uniform for a time series of 12 years or longer than for shorter ones. The standard deviation of PV declined to a minimum at 12–15 years, as the length of the time series increased. Discrimination of estimates of PV was reliable for 15-year time series and longer, but not necessarily for shorter ones. Although M. euphorbiae had a relatively low PV, the coefficient of variation of that PV (12.5), was higher than for the other two species (3.5, 4.5). For robust estimates of PV, a time series of 15 years is recommended, because it minimises the standard deviation of PV, and discriminates values of PV that differ by 0.06 on a 0–1 scale.

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Uozumi, Jun, and Toshimitsu Asakura. "Estimation Errors of Component Spectra Estimated by Means of the Concentration-Spectrum Correlation: Part I." Applied Spectroscopy 43, no. 1 (January 1989): 74–80. http://dx.doi.org/10.1366/0003702894201897.

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It is shown by theoretical analysis and computer simulations that statistical errors accompany the estimates of component spectra of complex mixtures calculated by the concentration-spectrum correlation method. It is revealed that the estimation errors consist of a superposition of other component spectra, each multiplied by a weighting factor. The weighting factor contains three statistical parameters of the sample: two sample standard deviations of both the objective and the interfering components, and the sample correlation coefficient between these two component concentrations. The probability density function of the weighting factor, as well as its ensemble average and standard deviation, is derived. It is shown that the ensemble standard deviation of estimation errors, which is a good measure for the accuracy of the estimated spectrum, can be estimated by the nonparametric method called a bootstrap. The behavior of the estimation errors and the effectiveness of the bootstrap method are demonstrated by computer simulations.

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35

ISLAM, MISBAH UL, M. SHAKEEL BILAL, T. ABBAS, M. U. RANA, and S. MOHSIN RAZA. "EMPIRICAL ESTIMATES OF PHYSICAL PARAMETERS FROM ELECTRICAL RESISTIVITY MEASUREMENTS ON FERRITES." Modern Physics Letters B 10, no. 07 (March 20, 1996): 299–303. http://dx.doi.org/10.1142/s0217984996000341.

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Measurements on the electrical resistivity of Mn 1−x Zn x Fe 2 O 4 ferrites with 0<x< 0.15 in the temperature range 300 K <T<450 K , have been carried out. Analysis of the normalised electrical resistivity of these ferrites shows deviations from linearity both at low and high temperatures. There exists a deviation in the electrical resistivity at 300 K at high zinc concentration which may be due to hopping of electrons between Fe +2 and Fe +3 ions at octahedral sites.

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36

Goryainov, V. B., and W. M. Khing. "Exponential Autoregressive Parameters Estimation." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 5 (86) (October 2019): 4–18. http://dx.doi.org/10.18698/1812-3368-2019-5-4-18.

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The purpose of the research was to compare the least squares estimatate and the least absolute deviation estimate depending on the probability distribution of the renewal process of the autoregressive equation. To achieve this goal, the sequence of observations of the exponential autoregressive process was repeatedly reproduced using computer simulation, and the least squares estimate and the least absolute deviation estimate were calculated for each sequence. The resulting estimation sequences were used to calculate the sample variances of the least squares estimate and the least absolute deviation estimate. The best estimate was the one with the lowest sample variance. The quantitative measure for the estimates comparison was the sample relative efficiency of estimates, defined as the inverse ratio of their sample variances. Normal distribution, contaminated normal distribution, i.e. Tukey distribution, with different values of the proportion and intensity of contamination, logistic distribution, Laplace distribution and Student distribution with different degrees of freedom, in particular, with one degree of freedom, that is, Cauchy distribution, were used as models of probability distribution of the renewal process. For each probability distribution, asymptotic values of the sample relative efficiency were obtained with an unlimited increase in the sample size of the observations of the autoregressive process. Findings of research show that the least absolute deviation estimate is better than the least squares estimate for Laplace distribution and the contaminated normal distribution with sufficiently large levels of the proportion and intensity of contamination. In other cases, the least squares estimate is preferable.

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Yao, Nian. "Optimal leverage ratio estimate of various models for leveraged ETFs to exceed a target: Probability estimates of large deviations." International Journal of Financial Engineering 05, no. 02 (June 2018): 1850016. http://dx.doi.org/10.1142/s2424786318500160.

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In this paper, we study the deviation probability estimate for a leveraged exchanged-traded fund (LETF). By large deviation principle, we derive explicitly the logarithmic limit of the tail probability when the price of a LETF exceeds a given reference asset, which allows us to compute the underlying leverage ratio. Then we apply our results to various existing models, including the geometric Brownian motion (GBM) model, generalized autoregressive conditional heteroskedasticity (GARCH) model, inverse GARCH model, extended Cox–Ingersoll–Ross (CIR) model, 3/2 model, as well as the Heston and 3/2 stochastic volatility models, and to present their corresponding optimal leverage ratios, respectively.

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38

Nagai, Hideo. "Robust estimates of certain large deviation probabilities for controlled semi-martingales." Banach Center Publications 105 (2015): 159–92. http://dx.doi.org/10.4064/bc105-0-11.

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Kosov, E. D. "Lower estimates of measure of deviation of polynomials from mathematical expectations." Doklady Mathematics 92, no. 3 (November 2015): 698–700. http://dx.doi.org/10.1134/s1064562415060162.

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Catoni, Olivier. "Rough Large Deviation Estimates for Simulated Annealing: Application to Exponential Schedules." Annals of Probability 20, no. 3 (July 1992): 1109–46. http://dx.doi.org/10.1214/aop/1176989682.

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41

N'zi, Modeste. "On large deviation estimates for two parameter diffusion processes and applications." Stochastics and Stochastic Reports 50, no. 1-2 (September 1994): 65–83. http://dx.doi.org/10.1080/17442509408833928.

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42

Caramellino, Lucia, and Barbara Pacchiarotti. "Large deviation estimates of the crossing probability for pinned Gaussian processes." Advances in Applied Probability 40, no. 2 (June 2008): 424–53. http://dx.doi.org/10.1239/aap/1214950211.

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The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in n fixed points at n fixed past instants. In particular, functional large deviation results are stated for small time. Several examples are considered: integrated or not fractional Brownian motions and m-fold integrated Brownian motion. As an application, the asymptotic behavior of the exit probability is studied and used for the practical purpose of the numerical computation, via Monte Carlo methods, of the hitting probability up to a given time of the unpinned process.

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Brändle, Cristina, and Emmanuel Chasseigne. "Large deviation estimates for some nonlocal equations. General bounds and applications." Transactions of the American Mathematical Society 365, no. 7 (February 7, 2013): 3437–76. http://dx.doi.org/10.1090/s0002-9947-2013-05629-2.

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44

Caramellino, Lucia, and Barbara Pacchiarotti. "Large deviation estimates of the crossing probability for pinned Gaussian processes." Advances in Applied Probability 40, no. 02 (June 2008): 424–53. http://dx.doi.org/10.1017/s0001867800002597.

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The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in n fixed points at n fixed past instants. In particular, functional large deviation results are stated for small time. Several examples are considered: integrated or not fractional Brownian motions and m-fold integrated Brownian motion. As an application, the asymptotic behavior of the exit probability is studied and used for the practical purpose of the numerical computation, via Monte Carlo methods, of the hitting probability up to a given time of the unpinned process.

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45

Bhatia, Manan. "Moderate Deviation and Exit Time Estimates for Stationary Last Passage Percolation." Journal of Statistical Physics 181, no. 4 (September 9, 2020): 1410–32. http://dx.doi.org/10.1007/s10955-020-02632-x.

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46

Lin, Mau-Wei, James F. Watson, and James R. Baggett. "Inheritance of Soluble Solids and Pyruvic Acid Content of Bulb Onions." Journal of the American Society for Horticultural Science 120, no. 1 (January 1995): 119–22. http://dx.doi.org/10.21273/jashs.120.1.119.

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Analysis of parents and progeny generations of bulb onion (Allium cepa L.) crosses among parents with differing content of soluble solids (SS) and pyruvic acid (PA) showed that SS and PA are expressed and inherited in a quantitative manner. Distribution of SS and PA in both parents and progenies covered a range of values. Generation means, frequency distributions, deviation from midparent value, and estimates of gene effects all indicated that inheritance of SS and PA was additive, except for small deviations from the additive hypothesis in several individual backcrosses. Estimates of broad-sense heritability ranged from 48% to 53% for PA and 8 % to 56 % for SS. Phenotypic correlations between PA and SS estimated from the F2 generations of two crosses, were moderate and positive (r = 0.50 and 0.42).

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47

Stier, P., N. A. J. Schutgens, H. Bian, O. Boucher, M. Chin, S. Ghan, N. Huneeus, et al. "Host model uncertainties in aerosol radiative forcing estimates: results from the AeroCom prescribed intercomparison study." Atmospheric Chemistry and Physics Discussions 12, no. 9 (September 25, 2012): 25487–549. http://dx.doi.org/10.5194/acpd-12-25487-2012.

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Abstract. Simulated multi-model "diversity" in aerosol direct radiative forcing estimates is often perceived as measure of aerosol uncertainty. However, current models used for aerosol radiative forcing calculations vary considerably in model components relevant for forcing calculations and the associated "host-model uncertainties" are generally convoluted with the actual aerosol uncertainty. In this AeroCom Prescribed intercomparison study we systematically isolate and quantify host model uncertainties on aerosol forcing experiments through prescription of identical aerosol radiative properties in nine participating models. Even with prescribed aerosol radiative properties, simulated clear-sky and all-sky aerosol radiative forcings show significant diversity. For a purely scattering case with globally constant optical depth of 0.2, the global-mean all-sky top-of-atmosphere radiative forcing is −4.51 W m−2 and the inter-model standard deviation is 0.70 W m−2, corresponding to a relative standard deviation of 15%. For a case with partially absorbing aerosol with an aerosol optical depth of 0.2 and single scattering albedo of 0.8, the forcing changes to 1.26 W m−2, and the standard deviation increases to 1.21 W m−2, corresponding to a significant relative standard deviation of 96%. However, the top-of-atmosphere forcing variability owing to absorption is low, with relative standard deviations of 9% clear-sky and 12% all-sky. Scaling the forcing standard deviation for a purely scattering case to match the sulfate radiative forcing in the AeroCom Direct Effect experiment, demonstrates that host model uncertainties could explain about half of the overall sulfate forcing diversity of 0.13 W m−2 in the AeroCom Direct Radiative Effect experiment. Host model errors in aerosol radiative forcing are largest in regions of uncertain host model components, such as stratocumulus cloud decks or areas with poorly constrained surface albedos, such as sea ice. Our results demonstrate that host model uncertainties are an important component of aerosol forcing uncertainty that require further attention.

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Stier, P., N. A. J. Schutgens, N. Bellouin, H. Bian, O. Boucher, M. Chin, S. Ghan, et al. "Host model uncertainties in aerosol radiative forcing estimates: results from the AeroCom Prescribed intercomparison study." Atmospheric Chemistry and Physics 13, no. 6 (March 20, 2013): 3245–70. http://dx.doi.org/10.5194/acp-13-3245-2013.

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Abstract. Simulated multi-model "diversity" in aerosol direct radiative forcing estimates is often perceived as a measure of aerosol uncertainty. However, current models used for aerosol radiative forcing calculations vary considerably in model components relevant for forcing calculations and the associated "host-model uncertainties" are generally convoluted with the actual aerosol uncertainty. In this AeroCom Prescribed intercomparison study we systematically isolate and quantify host model uncertainties on aerosol forcing experiments through prescription of identical aerosol radiative properties in twelve participating models. Even with prescribed aerosol radiative properties, simulated clear-sky and all-sky aerosol radiative forcings show significant diversity. For a purely scattering case with globally constant optical depth of 0.2, the global-mean all-sky top-of-atmosphere radiative forcing is −4.47 Wm−2 and the inter-model standard deviation is 0.55 Wm−2, corresponding to a relative standard deviation of 12%. For a case with partially absorbing aerosol with an aerosol optical depth of 0.2 and single scattering albedo of 0.8, the forcing changes to 1.04 Wm−2, and the standard deviation increases to 1.01 W−2, corresponding to a significant relative standard deviation of 97%. However, the top-of-atmosphere forcing variability owing to absorption (subtracting the scattering case from the case with scattering and absorption) is low, with absolute (relative) standard deviations of 0.45 Wm−2 (8%) clear-sky and 0.62 Wm−2 (11%) all-sky. Scaling the forcing standard deviation for a purely scattering case to match the sulfate radiative forcing in the AeroCom Direct Effect experiment demonstrates that host model uncertainties could explain about 36% of the overall sulfate forcing diversity of 0.11 Wm−2 in the AeroCom Direct Radiative Effect experiment. Host model errors in aerosol radiative forcing are largest in regions of uncertain host model components, such as stratocumulus cloud decks or areas with poorly constrained surface albedos, such as sea ice. Our results demonstrate that host model uncertainties are an important component of aerosol forcing uncertainty that require further attention.

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Slabospitsky, A. "Recurrent algorithm for non-stationary parameter estimation by least squares method with least deviations from ‘attraction’ points for bilinear discrete dynamic systems." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2018): 71–74. http://dx.doi.org/10.17721/1812-5409.2018/3.10.

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The estimation problem of slowly time-varying parameter matrices is considered for bilinear discrete dynamic system in the presence of disturbances. The least squares estimate with variable forgetting factor is investigated for this object in non-classical situation when this estimate may be not unique and additionally ‘attraction’ points for unknown parameter matrices are given at any moment. The set of all above-mentioned estimates of these unknown matrices is defined through the Moore-Penrose pseudo-inverse operator. The least squares estimate with variable forgetting factor and least deviation norm from given ‘attraction’ point at any moment is proposed as unique estimate on this set of all estimates. The explicit form of representation is obtained for this unique estimate of the parameter matrices by the least squares method with variable forgetting factor and least deviation norm from given ‘attraction’ points under non-classical assumptions. The recurrent algorithm for this estimate is also derived which does not require the usage of the matrix pseudo-inverse operator.

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50

Liu, Pei-Dong, Min Qian, and Yang Zhao. "Large deviations in Axiom A endomorphisms." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 6 (December 2003): 1379–88. http://dx.doi.org/10.1017/s0308210500002997.

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