Artykuły w czasopismach: „Variance model”

1

Kubáček, Lubomír. "Linear model with inaccurate variance components". Applications of Mathematics 41, nr 6 (1996): 433–45. http://dx.doi.org/10.21136/am.1996.134336.

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Volaufová, Júlia. "On variance of the two-stage estimator in variance-covariance components model". Applications of Mathematics 38, nr 1 (1993): 1–9. http://dx.doi.org/10.21136/am.1993.104529.

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Pardavi-Horvath, M., E. Della Torre i F. Vajda. "A variable variance Preisach model (garnet film)". IEEE Transactions on Magnetics 29, nr 6 (listopad 1993): 3793–95. http://dx.doi.org/10.1109/20.281302.

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Zainodin, H. J., G. Khuneswari, A. Noraini i F. A. A. Haider. "Selected Model Systematic Sequence via Variance Inflationary Factor". International Journal of Applied Physics and Mathematics 5, nr 2 (2015): 105–14. http://dx.doi.org/10.17706/ijapm.2015.5.2.105-114.

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Bishop, Craig H., i Elizabeth A. Satterfield. "Hidden Error Variance Theory. Part I: Exposition and Analytic Model". Monthly Weather Review 141, nr 5 (1.05.2013): 1454–68. http://dx.doi.org/10.1175/mwr-d-12-00118.1.

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Abstract A conundrum of predictability research is that while the prediction of flow-dependent error distributions is one of its main foci, chaos fundamentally hides flow-dependent forecast error distributions from empirical observation. Empirical estimation of such error distributions requires a large sample of error realizations given the same flow-dependent conditions. However, chaotic elements of the flow and the observing network make it impossible to collect a large enough conditioned error sample to empirically define such distributions and their variance. Such conditional variances are “hidden.” Here, an exposition of the problem is developed from an ensemble Kalman filter data assimilation system applied to a 10-variable nonlinear chaotic model and 25 000 replicate models. The 25 000 replicates reveal the error variances that would otherwise be hidden. It is found that the inverse-gamma distribution accurately approximates the posterior distribution of conditional error variances given an imperfect ensemble variance and provides a reasonable approximation to the prior climatological distribution of conditional error variances. A new analytical model shows how the properties of a likelihood distribution of ensemble variances given a true conditional error variance determine the posterior distribution of error variances given an ensemble variance. The analytically generated distributions are shown to satisfactorily fit empirically determined distributions. The theoretical analysis yields a rigorous interpretation and justification of hybrid error variance models that linearly combine static and flow-dependent estimates of forecast error variance; in doing so, it also helps justify and inform hybrid error covariance models.

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6

Borcia, I. D., L. Spinu i A. Stancu. "A Preisach-Neel model with thermally variable variance". IEEE Transactions on Magnetics 38, nr 5 (wrzesień 2002): 2415–17. http://dx.doi.org/10.1109/tmag.2002.803611.

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7

Hjalmarsson, H. "A Model Variance Estimator". IFAC Proceedings Volumes 26, nr 2 (lipiec 1993): 335–40. http://dx.doi.org/10.1016/s1474-6670(17)49139-7.

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Koul, Hira L., i Weixing Song. "Conditional variance model checking". Journal of Statistical Planning and Inference 140, nr 4 (kwiecień 2010): 1056–72. http://dx.doi.org/10.1016/j.jspi.2009.10.008.

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9

Stuchlý, Jaroslav. "Bayes unbiased estimation in a model with two variance components". Applications of Mathematics 32, nr 2 (1987): 120–30. http://dx.doi.org/10.21136/am.1987.104241.

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10

Stuchlý, Jaroslav. "Bayes unbiased estimation in a model with three variance components". Applications of Mathematics 34, nr 5 (1989): 375–86. http://dx.doi.org/10.21136/am.1989.104365.

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11

Zvára, Karel. "Analysis of variance as regression model with a reparametrization restriction". Applications of Mathematics 37, nr 6 (1992): 453–58. http://dx.doi.org/10.21136/am.1992.104523.

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12

Kudeláš, Jaromír. "The linear model with variance-covariance components and jackknife estimation". Applications of Mathematics 39, nr 2 (1994): 111–25. http://dx.doi.org/10.21136/am.1994.134248.

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13

Zhu, Jun, i Bruce S. Weir. "Mixed model approaches for diallel analysis based on a bio-model". Genetical Research 68, nr 3 (grudzień 1996): 233–40. http://dx.doi.org/10.1017/s0016672300034200.

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SummaryA MINQUE(l) procedure, which is minimum norm quadratic unbiased estimation (MINQUE) method with 1 for all the prior values, is suggested for estimating variance and covariance components in a bio-model for diallel crosses. Unbiasedness and efficiency of estimation were compared for MINQUE(l), restricted maximum likelihood (REML) and MINQUE(θ) which has parameter values for the prior values. MINQUE(l) is almost as efficient as MINQUE(θ) for unbiased estimation of genetic variance and covariance components. The bio-model is efficient and robust for estimating variance and covariance components for maternal and paternal effects as well as for nuclear effects. A procedure of adjusted unbiased prediction (AUP) is proposed for predicting random genetic effects in the bio-model. The jack-knife procedure is suggested for estimation of sampling variances of estimated variance and covariance components and of predicted genetic effects. Worked examples are given for estimation of variance and covariance components and for prediction of genetic merits.

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14

Carr, P., i A. Itkin. "Geometric Local Variance Gamma Model". Journal of Derivatives 27, nr 2 (11.09.2019): 7–30. http://dx.doi.org/10.3905/jod.2019.1.084.

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Arias-Castro, Ery, i Rong Huang. "The sparse variance contamination model". Statistics 54, nr 5 (2.09.2020): 1081–93. http://dx.doi.org/10.1080/02331888.2020.1823394.

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Yuan, Ao, Guanjie Chen, Qi Yang, Charles Rotimi i George Bonney. "Variance components model with disequilibria". European Journal of Human Genetics 14, nr 8 (24.05.2006): 941–52. http://dx.doi.org/10.1038/sj.ejhg.5201645.

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Schoutens, Wim, i Geert Van Damme. "The β-variance gamma model". Review of Derivatives Research 14, nr 3 (24.07.2010): 263–82. http://dx.doi.org/10.1007/s11147-010-9057-y.

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18

Fung, Thomas, Joanna J. J. Wang i Eugene Seneta. "Contaminated Variance–Mean mixing model". Computational Statistics & Data Analysis 67 (listopad 2013): 258–67. http://dx.doi.org/10.1016/j.csda.2013.05.024.

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19

Sikström, Sverker. "The variance reaction time model". Cognitive Psychology 48, nr 4 (czerwiec 2004): 371–421. http://dx.doi.org/10.1016/j.cogpsych.2003.08.002.

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20

Likothanassis, Spiros D., i Sokratis K. Katsikas. "Multi-model minimum variance control". International Journal of Adaptive Control and Signal Processing 12, nr 6 (wrzesień 1998): 527–35. http://dx.doi.org/10.1002/(sici)1099-1115(199809)12:6<527::aid-acs510>3.0.co;2-g.

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21

Matsumoto, Koichi. "Mean–variance hedging with model risk". International Journal of Financial Engineering 04, nr 04 (grudzień 2017): 1750042. http://dx.doi.org/10.1142/s2424786317500426.

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This paper studies a hedging problem of a derivative security in a one-period model when there is the model risk. The hedging error is measured by a quadratic criterion. The model risk means that the true model is uncertain and there are many candidates for the true model. The true model is assumed to be in a set of models. We study an optimal strategy which minimizes the worst-case hedging error over all models in the set. We show how to calculate an optimal strategy and the minimum hedging error effectively. Finally we give some numerical examples to demonstrate the usefulness of our method.

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22

Lark, R. M. "Kriging a soil variable with a simple nonstationary variance model". Journal of Agricultural, Biological, and Environmental Statistics 14, nr 3 (wrzesień 2009): 301–21. http://dx.doi.org/10.1198/jabes.2009.07060.

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23

Mowrer, H. Todd. "Estimating components of propagated variance in growth simulation model projections". Canadian Journal of Forest Research 21, nr 3 (1.03.1991): 379–86. http://dx.doi.org/10.1139/x91-047.

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First-order Taylor series variance estimation equations were embedded in a growth simulation model to estimate propagated variances during growth and yield projections. Variance equations estimated three error components: covariances propagated through predictor variables, covariances from estimated regressor coefficients, and covariances between regressor coefficients and variables. A separate Monte Carlo process was used to estimate the total variance in projected variables caused by simultaneous perturbations in values of initialization variables and in regressor coefficients. Variances estimated by these two procedures were compared over five consecutive projection periods for six variables in a forest growth simulation model. While results agreed closely for the variance in mean stand diameter, disparities increased for other variables later in the model estimation sequence. Disparities were attributed to differences between the populations used in both variance estimation procedures and to possible violations of Taylor series assumptions in the variance estimation equations.

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24

Pahade, Jagdish Kumar, i Manoj Jha. "Credibilistic variance and skewness of trapezoidal fuzzy variable and mean–variance–skewness model for portfolio selection". Results in Applied Mathematics 11 (sierpień 2021): 100159. http://dx.doi.org/10.1016/j.rinam.2021.100159.

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Wan, Fei. "Analyzing pre-post designs using the analysis of covariance models with and without the interaction term in a heterogeneous study population". Statistical Methods in Medical Research 29, nr 1 (13.02.2019): 189–204. http://dx.doi.org/10.1177/0962280219827971.

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Pre-post parallel group randomized designs have been frequently used to compare the effectiveness of competing treatment strategies and the ordinary least squares (OLS)-based analysis of covariance model (ANCOVA) is a routine analytic approach. In many scenarios, the associations between the baseline and the post-randomization scores could differ between the treatment and control arms, which justifies the inclusion of the treatment by baseline score interaction in ANCOVA. This heterogeneity may also cause heteroscedastic errors in ANCOVA. In this study, we compared the performances of the ANCOVA models with and without the interaction term in estimating the marginal treatment effect in a heterogeneous two-arm pre-post design. We explored the relationship between the two nested ANCOVA models from the perspective of an omitted variable bias problem and further revealed the reasons why the usual ANCOVA may fail in heterogeneous scenario through the discussion of the three types of variances associated with the ANCOVA estimators of the marginal treatment effect: the target unconditional variance, the conditional variance allowing unequal error variances, and the OLS conditional variance derived under the assumption of constant error variance. We demonstrated analytically and with simulations that the proposed heteroscadastic-consistent variance estimators provide valid unconditional inference for ANCOVA, and the ANCOVA interaction model is more powerful than the ANCOVA main effect model when a design is unbalanced.

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26

Bishop, Craig H., Elizabeth A. Satterfield i Kevin T. Shanley. "Hidden Error Variance Theory. Part II: An Instrument That Reveals Hidden Error Variance Distributions from Ensemble Forecasts and Observations". Monthly Weather Review 141, nr 5 (1.05.2013): 1469–83. http://dx.doi.org/10.1175/mwr-d-12-00119.1.

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Abstract In Part I of this study, a model of the distribution of true error variances given an ensemble variance is shown to be defined by six parameters that also determine the optimal weights for the static and flow-dependent parts of hybrid error variance models. Two of the six parameters (the climatological mean of forecast error variance and the climatological minimum of ensemble variance) are straightforward to estimate. The other four parameters are (i) the variance of the climatological distribution of the true conditional error variances, (ii) the climatological minimum of the true conditional error variance, (iii) the relative variance of the distribution of ensemble variances given a true conditional error variance, and (iv) the parameter that defines the mean response of the ensemble variances to changes in the true error variance. These parameters are hidden because they are defined in terms of condition-dependent forecast error variance, which is unobservable if the condition is not sufficiently repeatable. Here, a set of equations that enable these hidden parameters to be accurately estimated from a long time series of (observation minus forecast, ensemble variance) data pairs is presented. The accuracy of the equations is demonstrated in tests using data from long data assimilation cycles with differing model error variance parameters as well as synthetically generated data. This newfound ability to estimate these hidden parameters provides new tools for assessing the quality of ensemble forecasts, tuning hybrid error variance models, and postprocessing ensemble forecasts.

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27

Goard, Joanna. "A Time-Dependent Variance Model for Pricing Variance and Volatility Swaps". Applied Mathematical Finance 18, nr 1 (17.02.2011): 51–70. http://dx.doi.org/10.1080/13504861003795019.

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Shen, Yang, Xin Zhang i Tak Kuen Siu. "Mean–variance portfolio selection under a constant elasticity of variance model". Operations Research Letters 42, nr 5 (lipiec 2014): 337–42. http://dx.doi.org/10.1016/j.orl.2014.05.008.

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Das, Kalyan. "Variance Component Estimation in General Mixed Model of Analysis of Variance". Calcutta Statistical Association Bulletin 34, nr 3-4 (wrzesień 1985): 131–44. http://dx.doi.org/10.1177/0008068319850301.

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Arora, Vivek K., i George J. Boer. "The Temporal Variability of Soil Moisture and Surface Hydrological Quantities in a Climate Model". Journal of Climate 19, nr 22 (15.11.2006): 5875–88. http://dx.doi.org/10.1175/jcli3926.1.

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Abstract The variance budget of land surface hydrological quantities is analyzed in the second Atmospheric Model Intercomparison Project (AMIP2) simulation made with the Canadian Centre for Climate Modelling and Analysis (CCCma) third-generation general circulation model (AGCM3). The land surface parameterization in this model is the comparatively sophisticated Canadian Land Surface Scheme (CLASS). Second-order statistics, namely variances and covariances, are evaluated, and simulated variances are compared with observationally based estimates. The soil moisture variance is related to second-order statistics of surface hydrological quantities. The persistence time scale of soil moisture anomalies is also evaluated. Model values of precipitation and evapotranspiration variability compare reasonably well with observationally based and reanalysis estimates. Soil moisture variability is compared with that simulated by the Variable Infiltration Capacity-2 Layer (VIC-2L) hydrological model driven with observed meteorological data. An equation is developed linking the variances and covariances of precipitation, evapotranspiration, and runoff to soil moisture variance via a transfer function. The transfer function is connected to soil moisture persistence in terms of lagged autocorrelation. Soil moisture persistence time scales are shorter in the Tropics and longer at high latitudes as is consistent with the relationship between soil moisture persistence and the latitudinal structure of potential evaporation found in earlier studies. In the Tropics, although the persistence of soil moisture anomalies is short and values of the transfer function small, high values of soil moisture variance are obtained because of high precipitation variability. At high latitudes, by contrast, high soil moisture variability is obtained despite modest precipitation variability since the persistence time scale of soil moisture anomalies is long. Model evapotranspiration estimates show little variability and soil moisture variability is dominated by precipitation and runoff, which account for about 90% of the soil moisture variance over land surface areas.

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Ledwina, Teresa, i Jan Mielniczuk. "Variance function estimation via model selection". Applicationes Mathematicae 37, nr 4 (2010): 387–411. http://dx.doi.org/10.4064/am37-4-1.

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32

Willems, P. "Model uncertainty analysis by variance decomposition". Physics and Chemistry of the Earth, Parts A/B/C 42-44 (styczeń 2012): 21–30. http://dx.doi.org/10.1016/j.pce.2011.07.003.

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Guillaume, Florence, i Wim Schoutens. "Heston Model: The Variance Swap Calibration". Journal of Optimization Theory and Applications 161, nr 1 (17.05.2013): 76–89. http://dx.doi.org/10.1007/s10957-013-0331-7.

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Tjärnström, F., i L. Ljung. "L2 Model reduction and variance reduction". Automatica 38, nr 9 (wrzesień 2002): 1517–30. http://dx.doi.org/10.1016/s0005-1098(02)00066-3.

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35

Ould Aly, S. M. "Forward Variance Dynamics: Bergomi’s Model Revisited". Applied Mathematical Finance 21, nr 1 (26.07.2013): 84–107. http://dx.doi.org/10.1080/1350486x.2013.812329.

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Fu, Yuting. "On Generalizations of Mean–Variance Model". Journal of Physics: Conference Series 1168 (luty 2019): 052011. http://dx.doi.org/10.1088/1742-6596/1168/5/052011.

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37

Green, Samuel B., Janet G. Marquis, Scott L. Hershberger, Marilyn S. Thompson i Karen M. McCollam. "The overparameterized analysis of variance model." Psychological Methods 4, nr 2 (1999): 214–33. http://dx.doi.org/10.1037/1082-989x.4.2.214.

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Kshirsagar, Anant M., i R. Radhakrishnan. "A note on variance components model". International Journal of Mathematical Education in Science and Technology 40, nr 2 (15.03.2009): 287–89. http://dx.doi.org/10.1080/00207390802276192.

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Wensch-Dorendorf, M., N. Mielenz, E. Groeneveld, M. Kovac i L. Schüler. "Varianzkomponentenschätzung unter Berücksichtigung von Dominanz an simulierten Reinzuchtlinien". Archives Animal Breeding 47, nr 4 (10.10.2004): 387–95. http://dx.doi.org/10.5194/aab-47-387-2004.

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Abstract. Title of the paper: Estimation of variance components under dominance with simulated purebred lines A stochastic simulation based on a gene model was used to investigate the estimation of variance with dominance and additive animal models. For a heritability in broad sense of 0.5 three ratios of dominance variance (5, 10 and 25%) on the phenotypic variance were investigated under different degrees of dominance. No additionally biased estimations of the variance components as consequence of different dominance degrees were found. By using the dominance model for random mating as well as for selection the differences between true parameters and estimation values were small for all dominance degrees and ratios of dominance variance. Small, but significantly, differences can be explained by the change of the allele frequencies over the generations due to the influence of selection. By using the additive animal model, that ignores the dominance relationship, for high ratios of the dominance variance (25% or greater) important biased estimations of the variances were observed. For dominance ratios of 5% no significantly overestimation of the additive variances with the reduced model were found under selection and random mating.

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40

Bt Abdul Halima, Nurfadhlina, Dwi Susanti, Alit Kartiwa i Endang Soeryana Hasbullah. "Abnormal Portfolio Asset Allocation Model: Review". International Journal of Business, Economics, and Social Development 1, nr 1 (12.06.2020): 46–54. http://dx.doi.org/10.46336/ijbesd.v1i1.18.

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It has been widely studied how investors will allocate their assets to an investment when the return of assets is normally distributed. In this context usually, the problem of portfolio optimization is analyzed using mean-variance. When asset returns are not normally distributed, the mean-variance analysis may not be appropriate for selecting the optimum portfolio. This paper will examine the consequences of abnormalities in the process of allocating investment portfolio assets. Here will be shown how to adjust the mean-variance standard as a basic framework for asset allocation in cases where asset returns are not normally distributed. We will also discuss the application of the optimum strategies for this problem. Based on the results of literature studies, it can be concluded that the expected utility approximation involves averages, variances, skewness, and kurtosis, and can be extended to even higher moments.

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Czaplewski, Raymond L., i David Bruce. "Retransformation bias in a stem profile model". Canadian Journal of Forest Research 20, nr 10 (1.10.1990): 1623–30. http://dx.doi.org/10.1139/x90-215.

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An unbiased profile model, fit to diameter divided by diameter at breast height, overestimated volume of 5.3-m log sections by 0.5 to 3.5%. Another unbiased profile model, fit to squared diameter divided by squared diameter at breast height, underestimated bole diameters by 0.2 to 2.1%. These biases are caused by retransformation of the predicted dependent variable; the degree of retransformation bias depends upon choice of dependent variable in the regression model, variance of its prediction errors, and the bole position of the desired prediction. Retransformation biases were greatest near the merchantable top of large trees. Equations are given that reduce the magnitude of these biases, but accurate variance models are required. Additional biases are identified for more complex transformations of stem profile models.

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Bruckner, T., M. Schumacher i M. Wolkewitz. "Accurate Variance Estimation for Prevalence Ratios". Methods of Information in Medicine 46, nr 05 (2007): 567–71. http://dx.doi.org/10.1160/me0416.

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Summary Objectives: The log-binomial model is recommended for calculating the prevalence ratio in cross-sectional studies with binary outcomes. However, convergence problems may occur as this model is numerically unstable. If this happens, the Poisson model should be used, but the Poisson model variance needsto be adjusted. Here, we compare different adjustments. Methods: Using simulation we evaluated the performance of Poisson models with i) a robust variance, ii) the scale parameter adjusted by Pearson’s chi-square, and iii) the scale parameter adjusted by the deviance. These models were compared with the log-binomial model with respectto hypothesis testing. Confounding and effect modification are considered. Results: All adjustment models improved the variance estimation. The Poisson model with a robust variance performed best. When the log-binomial model is numerically stable as well as unstable, this model yields reasonable power and type I error values. But the Poisson model with the scale parameter adjusted by Pearson’s chi-square also showed good results. Conclusions: When estimating prevalence ratios, if the log-binomial fails to converge, we recommend the Poisson modelwith a robust estimate of variance.

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Reich, Brian J., i James S. Hodges. "Identification of the variance components in the general two-variance linear model". Journal of Statistical Planning and Inference 138, nr 6 (lipiec 2008): 1592–604. http://dx.doi.org/10.1016/j.jspi.2007.05.046.

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Fortin, Mathieu, Rubén Manso i Robert Schneider. "Parametric bootstrap estimators for hybrid inference in forest inventories". Forestry: An International Journal of Forest Research 91, nr 3 (22.11.2017): 354–65. http://dx.doi.org/10.1093/forestry/cpx048.

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Abstract In forestry, the variable of interest is not always directly available from forest inventories. Consequently, practitioners have to rely on models to obtain predictions of this variable of interest. This context leads to hybrid inference, which is based on both the probability design and the model. Unfortunately, the current analytical hybrid estimators for the variance of the point estimator are mainly based on linear or nonlinear models and their use is limited when the model reaches a high level of complexity. An alternative consists of using a variance estimator based on resampling methods (Rubin, D. B. (1987). Multiple imputation for nonresponse surveys. John Wiley & Sons, Hoboken, New Jersey, USA). However, it turns out that a parametric bootstrap (BS) estimator of the variance can be biased in contexts of hybrid inference. In this study, we designed and tested a corrected BS estimator for the variance of the point estimator, which can easily be implemented as long as all of the stochastic components of the model can be properly simulated. Like previous estimators, this corrected variance estimator also makes it possible to distinguish the contribution of the sampling and the model to the variance of the point estimator. The results of three simulation studies of increasing complexity showed no evidence of bias for this corrected variance estimator, which clearly outperformed the BS variance estimator used in previous studies. Since the implementation of this corrected variance estimator is not much more complicated, we recommend its use in contexts of hybrid inference based on complex models.

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Shahsavani, D., i A. Grimvall. "Variance-based sensitivity analysis of model outputs using surrogate models". Environmental Modelling & Software 26, nr 6 (czerwiec 2011): 723–30. http://dx.doi.org/10.1016/j.envsoft.2011.01.002.

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Arbogast, Patrick G., i Edward J. Bedrick. "Model-Checking Techniques for Linear Models With Parametric Variance Functions". Technometrics 46, nr 4 (listopad 2004): 404–10. http://dx.doi.org/10.1198/004017004000000473.

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Purczyński, Jan, i Kamila Bednarz-Okrzyńska. "Goodness of Fit Measures of Models with Binary Dependent Variable which Take into Account Heteroskedasticity of a Random Element". Folia Oeconomica Stetinensia 18, nr 1 (1.06.2018): 182–94. http://dx.doi.org/10.2478/foli-2018-0014.

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Abstract The paper tackles a problem which arises during the analysis of binary models, and which is the heteroskedasticity of a random element manifested by the variable value of variance. In the paper, the following probability models, used in the analysis of a dichotomic variable, were considered: a logit model, probit model, and raybit model, which is a model proposed by the authors. The following measures of goodness of fit, present in the field literature, were considered: MSE, MAE, WMSE, and WMAE. A new measure of goodness of fit of a model was proposed, which limits the amplitude of varying values of variance.

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JAFFRÉZIC, FLORENCE, GUILLEMETTE MAROT, SÉVERINE DEGRELLE, ISABELLE HUE i JEAN-LOUIS FOULLEY. "A structural mixed model for variances in differential gene expression studies". Genetical Research 89, nr 1 (luty 2007): 19–25. http://dx.doi.org/10.1017/s0016672307008646.

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The importance of variance modelling is now widely known for the analysis of microarray data. In particular the power and accuracy of statistical tests for differential gene expressions are highly dependent on variance modelling. The aim of this paper is to use a structural model on the variances, which includes a condition effect and a random gene effect, and to propose a simple estimation procedure for these parameters by working on the empirical variances. The proposed variance model was compared with various methods on both real and simulated data. It proved to be more powerful than the gene-by-gene analysis and more robust to the number of false positives than the homogeneous variance model. It performed well compared with recently proposed approaches such as SAM and VarMixt even for a small number of replicates, and performed similarly to Limma. The main advantage of the structural model is that, thanks to the use of a linear mixed model on the logarithm of the variances, various factors of variation can easily be incorporated in the model, which is not the case for previously proposed empirical Bayes methods. It is also very fast to compute and is adapted to the comparison of more than two conditions.

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Jianwang, Hong, Ricardo A. Ramirez-Mendoza i Jorge de J. Lozoya Santos. "Combing Instrumental Variable and Variance Matching for Aircraft Flutter Model Parameters Identification". Shock and Vibration 2019 (21.10.2019): 1–12. http://dx.doi.org/10.1155/2019/4296091.

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When the observed input-output data are corrupted by the observed noises in the aircraft flutter stochastic model, we need to obtain the more exact aircraft flutter model parameters to predict the flutter boundary accuracy and assure flight safety. So, here we combine the instrumental variable method in system identification theory and variance matching in modern spectrum theory to propose a new identification strategy: instrumental variable variance method. In the aircraft flutter stochastic model, after introducing instrumental variable to develop a covariance function, a new criterion function, composed by a difference between the theory value and actual estimation value of the covariance function, is established. Now, the new criterion function based on the covariance function can be used to identify the unknown parameter vector in the transfer function form. Finally, we apply this new instrumental variable variance method to identify the transfer function in one electrical current loop of flight simulator and aircraft flutter model parameters. Several simulation experiments have been performed to demonstrate the effectiveness of the algorithm proposed in this paper.

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Ngugi, AM, Eben Maré i R. Kufakunesu. "Pricing variable annuity guarantees in South Africa under a Variance-Gamma model". South African Actuarial Journal 15, nr 1 (17.12.2015): 131. http://dx.doi.org/10.4314/saaj.v15i1.6.

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