Fast calculations of Jackknife covariance matrix estimator
DOI:
https://doi.org/10.17721/1812-5409.2021/1.3Keywords:
generalized estimation equations, asymptotic behavior, mixture model, non-linear regression, minimax weights, covariance estimatorAbstract
We consider data in which each observed subject belongs to one of different subpopulations (components). The true number of component which a subject belongs to is unknown, but the researcher knows the probabilities that a subject belongs to a given component (concentration of the component in the mixture). The concentrations are different for different observations. So the distribution of the observed data is a mixture of components’ distributions with varying concentrations. A set of variables is observed for each subject. Dependence between these variables is described by a nonlinear regression model. The coefficients of this model are different for different components. Normality of estimator for nonlinear regression parameters is demonstrated under general assumptions. A mixture of logistic regression models with continuous response is considered as an example. In the paper we construct confidence ellipsoids for the regression parameters based on the modified least squares estimators. The covariances of these estimators are estimated by the multiple modifications of jackknife technique. Performance of the obtained confidence ellipsoids is assessed by simulations.
Pages of the article in the issue: 27 - 36
Language of the article: Ukrainian
References
D. M. TITTETINGTON, A. F. SMITH, U. E. MAKOV (1985) Analysis of Finite Mixture Distributions. Wiley, New York
G.J. MCLACHLAN, D.PEEL (2000) Finite mixture models. Wiley-Interscience
R.E MAIBORODA (2003) Statistical analysis of mixtures. Kyiv University Publishers, Kyiv (in Ukrainian)
R.E. MAIBORODA, O.V. SUGAKOVA (2012) Statistics of mixtures with varying concentrations with application to DNA microarray data analysis. Journal of nonparametric statistics. 24 , No 1 201–205 (2012)
R.E MAIBORODA, D. LIUBASHENKO (2015) Linear regression by observations from mixture with varying concentrations, Kyiv National Taras Shevchenko University, Kyiv, Ukraine
R.E. MAIBORODA, O.V. SUGAKOVA (2019) Jackknife covariance matrix estimation for observations from mixture, Modern Stochastics: Theory and Applications
M. H. QUENOUILLE (1956) Notes on bias in estimation. Biometrika, 43, 353-60 .
J. W. TUKEY (1958) Bias and confidence in not quite large samples. The Annals of Mathematical Statistics. 29 (2): 614
V.O. MIROSHNYCHENKO (2019) Generalized least squares estimates for mixture of nonlinear regressions, Bulletin of Taras Shevchenko National University of Kyiv; Series: Physics Mathematics, 2019, 5
V.O. MIROSHNYCHENKO, R.E. MAIBORODA (2020) Asymptotic normality of modified LS estimator for mixture of nonlinear regressions Modern Stochastics: Theory and Applications, Vol.7, Iss.7 pp. 435 - 448
J. Shao (2007) Mathematical Statistics, Springer
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
