Relevant bibliographies by topics / Variance model

Academic literature on the topic 'Variance model'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Variance model"

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Kubáček, Lubomír. "Linear model with inaccurate variance components." Applications of Mathematics 41, no. 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, no. 1 (1993): 1–9. http://dx.doi.org/10.21136/am.1993.104529.

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Pardavi-Horvath, M., E. Della Torre, and F. Vajda. "A variable variance Preisach model (garnet film)." IEEE Transactions on Magnetics 29, no. 6 (November 1993): 3793–95. http://dx.doi.org/10.1109/20.281302.

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Zainodin, H. J., G. Khuneswari, A. Noraini, and F. A. A. Haider. "Selected Model Systematic Sequence via Variance Inflationary Factor." International Journal of Applied Physics and Mathematics 5, no. 2 (2015): 105–14. http://dx.doi.org/10.17706/ijapm.2015.5.2.105-114.

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Bishop, Craig H., and Elizabeth A. Satterfield. "Hidden Error Variance Theory. Part I: Exposition and Analytic Model." Monthly Weather Review 141, no. 5 (May 1, 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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Borcia, I. D., L. Spinu, and A. Stancu. "A Preisach-Neel model with thermally variable variance." IEEE Transactions on Magnetics 38, no. 5 (September 2002): 2415–17. http://dx.doi.org/10.1109/tmag.2002.803611.

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Hjalmarsson, H. "A Model Variance Estimator." IFAC Proceedings Volumes 26, no. 2 (July 1993): 335–40. http://dx.doi.org/10.1016/s1474-6670(17)49139-7.

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Koul, Hira L., and Weixing Song. "Conditional variance model checking." Journal of Statistical Planning and Inference 140, no. 4 (April 2010): 1056–72. http://dx.doi.org/10.1016/j.jspi.2009.10.008.

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Stuchlý, Jaroslav. "Bayes unbiased estimation in a model with two variance components." Applications of Mathematics 32, no. 2 (1987): 120–30. http://dx.doi.org/10.21136/am.1987.104241.

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Stuchlý, Jaroslav. "Bayes unbiased estimation in a model with three variance components." Applications of Mathematics 34, no. 5 (1989): 375–86. http://dx.doi.org/10.21136/am.1989.104365.

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Dissertations / Theses on the topic "Variance model"

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Xiao, Yan. "Evaluating Variance of the Model Credibility Index." Digital Archive @ GSU, 2007. http://digitalarchive.gsu.edu/math_theses/39.

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Model credibility index is defined to be a sample size under which the power of rejection equals 0.5. It applies goodness-of-fit testing thinking and uses a one-number summary statistic as an assessment tool in a false model world. The estimation of the model credibility index involves a bootstrap resampling technique. To assess the consistency of the estimator of model credibility index, we instead study the variance of the power achieved at a fixed sample size. An improved subsampling method is proposed to obtain an unbiased estimator of the variance of power. We present two examples to interpret the mechanics of building model credibility index and estimate its error in model selection. One example is two-way independent model by Pearson Chi-square test, and another example is multi-dimensional logistic regression model using likelihood ratio test.
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Prosser, Robert James. "Robustness of multivariate mixed model ANOVA." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/25511.

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In experimental or quasi-experimental studies in which a repeated measures design is used, it is common to obtain scores on several dependent variables on each measurement occasion. Multivariate mixed model (MMM) analysis of variance (Thomas, 1983) is a recently developed alternative to the MANOVA procedure (Bock, 1975; Timm, 1980) for testing multivariate hypotheses concerning effects of a repeated factor (called occasions in this study) and interaction between repeated and non-repeated factors (termed group-by-occasion interaction here). If a condition derived by Thomas (1983), multivariate multi-sample sphericity (MMS), regarding the equality and structure of orthonormalized population covariance matrices is satisfied (given multivariate normality and independence for distributions of subjects' scores), valid likelihood-ratio MMM tests of group-by-occasion interaction and occasions hypotheses are possible. To date, no information has been available concerning actual (empirical) levels of significance of such tests when the MMS condition is violated. This study was conducted to begin to provide such information. Departure from the MMS condition can be classified into three types— termed departures of types A, B, and C respectively: (A) the covariance matrix for population ℊ (ℊ = 1,...G), when orthonormalized, has an equal-diagonal-block form but the resulting matrix for population ℊ is unequal to the resulting matrix for population ℊ' (ℊ ≠ ℊ'); (B) the G populations' orthonormalized covariance matrices are equal, but the matrix common to the populations does not have equal-diagonal-block structure; or (C) one or more populations has an orthonormalized covariance matrix which does not have equal-diagonal-block structure and two or more populations have unequal orthonormalized matrices. In this study, Monte Carlo procedures were used to examine the effect of each type of violation in turn on the Type I error rates of multivariate mixed model tests of group-by-occasion interaction and occasions null hypotheses. For each form of violation, experiments modelling several levels of severity were simulated. In these experiments: (a) the number of measured variables was two; (b) the number of measurement occasions was three; (c) the number of populations sampled was two or three; (d) the ratio of average sample size to number of measured variables was six or 12; and (e) the sample size ratios were 1:1 and 1:2 when G was two, and 1:1:1 and 1:1:2 when G was three. In experiments modelling violations of types A and C, the effects of negative and positive sampling were studied. When type A violations were modelled and samples were equal in size, actual Type I error rates did not differ significantly from nominal levels for tests of either hypothesis except under the most severe level of violation. In type A experiments using unequal groups in which the largest sample was drawn from the population whose orthogonalized covariance matrix has the smallest determinant (negative sampling), actual Type I error rates were significantly higher than nominal rates for tests of both hypotheses and for all levels of violation. In contrast, empirical levels of significance were significantly lower than nominal rates in type A experiments in which the largest sample was drawn from the population whose orthonormalized covariance matrix had the largest determinant (positive sampling). Tests of both hypotheses tended to be liberal in experiments which modelled type B violations. No strong relationships were observed between actual Type I error rates and any of: severity of violation, number of groups, ratio of average sample size to number of variables, and relative sizes of samples. In equal-groups experiments modelling type C violations in which the orthonormalized pooled covariance matrix departed at the more severe level from equal-diagonal-block form, actual Type I error rates for tests of both hypotheses tended to be liberal. Findings were more complex under the less severe level of structural departure. Empirical significance levels did not vary with the degree of interpopulation heterogeneity of orthonormalized covariance matrices. In type C experiments modelling negative sampling, tests of both hypotheses tended to be liberal. Degree of structural departure did not appear to influence actual Type I error rates but degree of interpopulation heterogeneity did. Actual Type I error rates in type C experiments modelling positive sampling were apparently related to the number of groups. When two populations were sampled, both tests tended to be conservative, while for three groups, the results were more complex. In general, under all types of violation the ratio of average group size to number of variables did not greatly affect actual Type I error rates. The report concludes with suggestions for practitioners considering use of the MMM procedure based upon the findings and recommends four avenues for future research on Type I error robustness of MMM analysis of variance. The matrix pool and computer programs used in the simulations are included in appendices.
Education, Faculty of
Educational and Counselling Psychology, and Special Education (ECPS), Department of
Graduate
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Moravec, Radek. "Oceňování opcí a variance gama proces." Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-18707.

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The submitted work deals with option pricing. Mathematical approach is immediately followed by an economic interpretation. The main problem is to model the underlying uncertainities driving the stock price. Using two well-known valuation models, binomial model and Black-Scholes model, we explain basic principles, especially risk neutral pricing. Due to the empirical biases new models have been developped, based on pure jump process. Variance gamma process and its special symmetric case are presented.
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Abdumuminov, Shuhrat, and David Emanuel Esteky. "Black-Litterman Model: Practical Asset Allocation Model Beyond Traditional Mean-Variance." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-32427.

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This paper consolidates and compares the applicability and practicality of Black-Litterman model versus traditional Markowitz Mean-Variance model. Although well-known model such as Mean-Variance is academically sound and popular, it is rarely used among asset managers due to its deficiencies. To put the discussion into context we shed light on the improvement made by Fisher Black and Robert Litterman by putting the performance and practicality of both Black- Litterman and Markowitz Mean-Variance models into test. We will illustrate detailed mathematical derivations of how the models are constructed and bring clarity and profound understanding of the intuition behind the models. We generate two different portfolios, composing data from 10-Swedish equities over the course of 10-year period and respectively select 30-days Swedish Treasury Bill as a risk-free rate. The resulting portfolios orientate our discussion towards the better comparison of the performance and applicability of these two models and we will theoretically and geometrically illustrate the differences. Finally, based on extracted results of the performance of both models we demonstrate the superiority and practicality of Black-Litterman model, which in our particular case outperform traditional Mean- Variance model.
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Tjärnström, Fredrik. "Variance expressions and model reduction in system identification /." Linköping : Univ, 2002. http://www.bibl.liu.se/liupubl/disp/disp2002/tek730s.pdf.

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Finlay, Richard. "The Variance Gamma (VG) Model with Long Range Dependence." University of Sydney, 2009. http://hdl.handle.net/2123/5434.

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Doctor of Philosophy (PhD)
This thesis mainly builds on the Variance Gamma (VG) model for financial assets over time of Madan & Seneta (1990) and Madan, Carr & Chang (1998), although the model based on the t distribution championed in Heyde & Leonenko (2005) is also given attention. The primary contribution of the thesis is the development of VG models, and the extension of t models, which accommodate a dependence structure in asset price returns. In particular it has become increasingly clear that while returns (log price increments) of historical financial asset time series appear as a reasonable approximation of independent and identically distributed data, squared and absolute returns do not. In fact squared and absolute returns show evidence of being long range dependent through time, with autocorrelation functions that are still significant after 50 to 100 lags. Given this evidence against the assumption of independent returns, it is important that models for financial assets be able to accommodate a dependence structure.
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Robinson, Timothy J. "Dual Model Robust Regression." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/11244.

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In typical normal theory regression, the assumption of homogeneity of variances is often not appropriate. Instead of treating the variances as a nuisance and transforming away the heterogeneity, the structure of the variances may be of interest and it is desirable to model the variances. Aitkin (1987) proposes a parametric dual model in which a log linear dependence of the variances on a set of explanatory variables is assumed. Aitkin's parametric approach is an iterative one providing estimates for the parameters in the mean and variance models through joint maximum likelihood. Estimation of the mean and variance parameters are interrelatedas the responses in the variance model are the squared residuals from the fit to the means model. When one or both of the models (the mean or variance model) are misspecified, parametric dual modeling can lead to faulty inferences. An alternative to parametric dual modeling is to let the data completely determine the form of the true underlying mean and variance functions (nonparametric dual modeling). However, nonparametric techniques often result in estimates which are characterized by high variability and they ignore important knowledge that the user may have regarding the process. Mays and Birch (1996) have demonstrated an effective semiparametric method in the one regressor, single-model regression setting which is a "hybrid" of parametric and nonparametric fits. Using their techniques, we develop a dual modeling approach which is robust to misspecification in either or both of the two models. Examples will be presented to illustrate the new technique, termed here as Dual Model Robust Regression.
Ph. D.
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Roh, Kyoungmin. "Evolutionary variance of gene network model via simulated annealing." [Ames, Iowa : Iowa State University], 2008.

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Letsoalo, Marothi Peter. "Assessing variance components of multilevel models pregnancy data." Thesis, University of Limpopo, 2019. http://hdl.handle.net/10386/2873.

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Thesis (M. Sc. (Statistics)
Most social and health science data are longitudinal and additionally multilevel in nature, which means that response data are grouped by attributes of some cluster. Ignoring the differences and similarities generated by these clusters results to misleading estimates, hence motivating for a need to assess variance components (VCs) using multilevel models (MLMs) or generalised linear mixed models (GLMMs). This study has explored and fitted teenage pregnancy census data that were gathered from 2011 to 2015 by the Africa Centre at Kwa-Zulu Natal, South Africa. The exploration of these data revealed a two level pure hierarchy data structure of teenage pregnancy status for some years nested within female teenagers. To fit these data, the effects that census year (year) and three female characteristics (namely age (age), number of household membership (idhhms), number of children before observation year (nch) have on teenage pregnancy were examined. Model building of this work, firstly, fitted a logit gen eralised linear model (GLM) under the assumption that teenage pregnancy measurements are independent between females and secondly, fitted a GLMM or MLM of female random effect. A better fit GLMM indicated, for an additional year on year, a 0.203 decrease on the log odds of teenage pregnancy while GLM suggested a 0.21 decrease and 0.557 increase for each additional year on age and year, respectively. A GLM with only year effect uncovered a fixed estimate which is higher, by 0.04, than that of a better fit GLMM. The inconsistency in the effect of year was caused by a significant female cluster variance of approximately 0.35 that was used to compute the VCs. Given the effect of year, the VCs suggested that 9.5% of the differences in teenage pregnancy lies between females while 0.095 similarities (scale from 0 to 1) are for the same female. It was also revealed that year does not vary within females. Apart from the small differences between observed estimates of the fitted GLM and GLMM, this work produced evidence that accounting for cluster effect improves accuracy of estimates. Keywords: Multilevel Model, Generalised Linear Mixed Model, Variance Components, Hier archical Data Structure, Social Science Data, Teenage Pregnancy
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Brien, Christopher J. "Factorial linear model analysis." Title page, table of contents and summary only, 1992. http://thesis.library.adelaide.edu.au/public/adt-SUA20010530.175833.

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"February 1992" Bibliography: leaf 323-344. Electronic publication; Full text available in PDF format; abstract in HTML format. Develops a general strategy for factorial linear model analysis for experimental and observational studies, an iterative, four-stage, model comparison procedure. The approach is applicable to studies characterized as being structure-balanced, multitiered and based on Tjur structures unless the structure involves variation factors when it must be a regular Tjur structure. It covers a wide range of experiments including multiple-error, change-over, two-phase, superimposed and unbalanced experiments. Electronic reproduction.[Australia] :Australian Digital Theses Program,2001.
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Books on the topic "Variance model"

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Faraway, Julian J. Extending Linear Model With R. London: Chapman & Hall/CRC, 2004.

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Schlicht, Ekkehart. Variance estimation in a random coefficients model. Bonn, Germany: IZA, 2006.

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Chang-Jin, Kim. In search of a model that an ARCH-type model may be approximating: The Markov model of heteroskedasticity. [Toronto, Ont: York University, Dept. of Economics, 1990.

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Hastie, Trevor. Exploring the nature of covariate effects in the proportional hazards model. Toronto: University of Toronto, Dept. of statistics, 1988.

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Boylan, John E. The compound Poisson demand model and the quadratic variance law. Coventry: University of Warwick. Warwick Business School Research Bureau, 1994.

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Extending the linear model with R: Generalized linear, mixed effects and nonparametric regression models. Boca Raton: Taylor & Francis, 2016.

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McEntegart, Karen. A comparison of mean-variance and mean-semivariance capital asset models : evidence from the Irish stock market. Dublin: University College Dublin, 1994.

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Park, Hun Y. A comparison of a random variance model and the Black-Scholes model of pricing long-term European options. [Urbana, Ill.]: College of Commerce and Business Administration, University of Illinois at Urbana-Champaign, 1991.

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Data analysis and approximate models: Model choice, location-scale, analysis of variance, nonparametic regression and image analysis. Boca Raton: CRC Press, 2014.

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Johansen, Søren. The asymptotic variance of the estimated roots in a cointegrated vector autoregressive model. Florence: European University Institute, Department of Economics, 2001.

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Book chapters on the topic "Variance model"

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Särndal, Carl-Erik, Bengt Swensson, and Jan Wretman. "Variance Estimation." In Model Assisted Survey Sampling, 418–46. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-4378-6_11.

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Hangay, George, Susan V. Gruner, F. W. Howard, John L. Capinera, Eugene J. Gerberg, Susan E. Halbert, John B. Heppner, et al. "Mean-Variance Model." In Encyclopedia of Entomology, 2313. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-6359-6_1761.

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Zimmerman, Dale L. "Inference for Variance–Covariance Parameters." In Linear Model Theory, 451–86. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52063-2_16.

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Zimmerman, Dale L. "Inference for Variance–Covariance Parameters." In Linear Model Theory, 325–50. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52074-8_16.

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Chung, Kai Lai, and Farid AitSahlia. "Mean-Variance Pricing Model." In Undergraduate Texts in Mathematics, 329–58. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-0-387-21548-8_9.

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Jalili-Kharaajoo, Mahdi, and Farhad Besharati. "Fuzzy Variance Analysis Model." In Computer and Information Sciences - ISCIS 2003, 537–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-39737-3_67.

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Qin, Zhongfeng. "Credibilistic Mean-Variance-Skewness Model." In Uncertainty and Operations Research, 29–52. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-1810-7_2.

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Qin, Zhongfeng. "Uncertain Random Mean-Variance Model." In Uncertainty and Operations Research, 131–49. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-1810-7_8.

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Board, John L. G., Charles M. S. Sutcliffe, and William T. Ziemba. "Portfolio Theory: Mean-Variance Model." In Encyclopedia of Operations Research and Management Science, 1142–48. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4419-1153-7_775.

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Malley, James D. "Linearization of the Basic Model." In Optimal Unbiased Estimation of Variance Components, 15–28. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4615-7554-2_3.

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Conference papers on the topic "Variance model"

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Pardavi-horvath, M., E. Della Terre, F. Vajda, and G. Verrtesy. "A Variable-variance Preisach Model." In 1993 Digests of International Magnetics Conference. IEEE, 1993. http://dx.doi.org/10.1109/intmag.1993.642266.

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Brinckman, Kevin, William Calhoon, Stephen Mattick, Jeremy Tomes, and Sanford Dash. "Scalar Variance Model Validation for High-Speed Variable Composition Flows." In 44th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2006. http://dx.doi.org/10.2514/6.2006-715.

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Jiang, Wendy Xi, Barry L. Nelson, and L. Jeff Hong. "Estimating Sensitivity to Input Model Variance." In 2019 Winter Simulation Conference (WSC). IEEE, 2019. http://dx.doi.org/10.1109/wsc40007.2019.9004684.

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Wan, Shuping. "Mean-variance Portfolio Model with Consumption." In 2006 9th International Conference on Control, Automation, Robotics and Vision. IEEE, 2006. http://dx.doi.org/10.1109/icarcv.2006.345085.

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Hoe, Lam Weng, and Lam Weng Siew. "Portfolio optimization with mean-variance model." In INNOVATIONS THROUGH MATHEMATICAL AND STATISTICAL RESEARCH: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4952526.

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Chen, Guohua, and Xiaolian Liao. "Credibility Mean-Variance-skewness Portfolio Selection Model." In 2010 2nd International Workshop on Database Technology and Applications (DBTA). IEEE, 2010. http://dx.doi.org/10.1109/dbta.2010.5659059.

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Pan, Qiming, and Xiaoxia Huang. "Mean-Variance Model for International Portfolio Selection." In 2008 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing (EUC). IEEE, 2008. http://dx.doi.org/10.1109/euc.2008.16.

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Mahdi Jalili Kharaajoo, Mahdi Jalili Kharaajoo, and Hassan Ebrahimirad Hassan Ebrahimirad. "A note on fuzzy variance analysis model." In 2003 International Symposium on Signals, Circuits and Systems. IEEE, 2003. http://dx.doi.org/10.1109/scs.2003.1226960.

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Bahnas, Mohamed, and Mohamed Al-Imam. "OPC model calibration considerations for data variance." In SPIE Advanced Lithography. SPIE, 2008. http://dx.doi.org/10.1117/12.776896.

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Boone-Sifuentes, Tanya, Antonio Robles-Kelly, and Asef Nazari. "Max-Variance Convolutional Neural Network Model Compression." In 2020 Digital Image Computing: Techniques and Applications (DICTA). IEEE, 2020. http://dx.doi.org/10.1109/dicta51227.2020.9363347.

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Reports on the topic "Variance model"

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West, Kenneth. A Variance Bounds Test of the Linear Quardractic Inventory Model. Cambridge, MA: National Bureau of Economic Research, March 1985. http://dx.doi.org/10.3386/w1581.

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Gelfand, Alan E., and Dipak K. Dey. Improved Estimation of the Disturbance Variance in a Linear Regression Model. Fort Belvoir, VA: Defense Technical Information Center, July 1989. http://dx.doi.org/10.21236/ada210272.

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Tong, C. Toward a more robust variance-based global sensitivity analysis of model outputs. Office of Scientific and Technical Information (OSTI), October 2007. http://dx.doi.org/10.2172/923115.

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Rauscher, Harold M. The microcomputer scientific software series 3: general linear model--analysis of variance. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Forest Experiment Station, 1985. http://dx.doi.org/10.2737/nc-gtr-86.

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Stock, James, and Mark Watson. Asymptotically Median Unbiased Estimation of Coefficient Variance in a Time Varying Parameter Model. Cambridge, MA: National Bureau of Economic Research, August 1996. http://dx.doi.org/10.3386/t0201.

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Hacker, Joshua P., Cari G. Kaufman, and James Hansen. State-Space Analysis of Model Error: A Probabilistic Parameter Estimation Framework with Spatial Analysis of Variance. Fort Belvoir, VA: Defense Technical Information Center, September 2012. http://dx.doi.org/10.21236/ada574466.

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Nelson, Charles, and Chang-Jin Kim. The Time-Varying-Parameter Model as an Alternative to ARCH for Modeling Changing Conditional Variance: The Case of Lucas Hypothesis. Cambridge, MA: National Bureau of Economic Research, September 1988. http://dx.doi.org/10.3386/t0070.

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Odom, Robert I. Seabed Variability and Its Influence on Acoustic Prediction Uncertainty Model and Data Variance and Resolution: How Do We Quantify Uncertainty? Fort Belvoir, VA: Defense Technical Information Center, August 2002. http://dx.doi.org/10.21236/ada628078.

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Odom, Robert I. Seabed Variability and its Influence on Acoustic Prediction Uncertainty. Model and Data Variance and Resolution: How Do We Quantify Uncertainty? Fort Belvoir, VA: Defense Technical Information Center, September 2003. http://dx.doi.org/10.21236/ada630037.

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Odom, Robert I. Seabed Variability and its Influence on Acoustic Prediction Uncertainty Model and Data Variance and Resolution: How Do We Quantify Uncertainty? Fort Belvoir, VA: Defense Technical Information Center, August 2002. http://dx.doi.org/10.21236/ada627080.

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