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), 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.
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