A Comparison of Error Variance Estimates in Nonparametric Mixed Models

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) wit...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2012-02, Vol.41 (4), p.778-790
Main Author: Li, Zaixing
Format: Article
Language:English
Subjects:
Asymptotic properties
Consistency
Error variance
Errors
Estimates
Estimators
Exact sciences and technology
General topics
Linear inference, regression
Mathematics
Mean square errors
MSE
NMMs
Nonparametric inference
Probability and statistics
Random errors
Sciences and techniques of general use
Smoothing
Statistics
Studies
Variance
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Summary: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 ), are inconsistent in NMMs. Besides, the equivalence of GCV proposed by Gu and Ma ( 2005 ) and GCV by Wang ( 1998b ) is also found. A simulation study is conducted to investigate the performance of these estimators.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2010.529526