Title: A Comparison of Error Variance Estimates in Nonparametric Mixed Models
Abstract: Abstract The author provides three kinds of estimates (six estimators) of the error variance in nonparametric mixed models (NMMs) without any distribution assumptions about random effects and random errors. Their asymptotic mean square errors are investigated. Different from nonparametric regression (NR) with independent homoscedastic case, error variance estimators by a nonparametric fit with the form of Y τ M σ Y/tr(M σ), which are consistent in NR (Dette et al., 1998 Dette , H. , Munk , A. , Wagner , T. ( 1998 ). Estimating the variance in nonparametric regression—what is a reasonable choice? J. R. Statist. Soc. B 60 : 751 – 764 .[Crossref] , [Google Scholar]), are inconsistent in NMMs. Besides, the equivalence of GCV proposed by Gu and Ma (2005 Gu , C. , Ma , P. ( 2005 ). Optimal smoothing in nonparametric mixed-effect models . Ann. Statist. 33 : 1357 – 1379 .[Crossref], [Web of Science ®] , [Google Scholar]) and GCV by Wang (1998b Wang , Y. ( 1998b ). Smoothing spline models with correlated random errors . J. Amer. Stat. Assoc. 93 : 341 – 348 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is also found. A simulation study is conducted to investigate the performance of these estimators. Keywords: ConsistencyError varianceMSENMMsMathematics Subject Classification: 62G0562G08 Acknowledgment This research was supported by the National Natural Science Foundation of China (No. 11001267) and by the Fundamental Research Funds for the Central Universities of China (No. 2009QS02).
Publication Year: 2012
Publication Date: 2012-02-15
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 3
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