BibTeX
@MISC{Chen12sieveinference,
author = {Xiaohong Chen and Zhipeng Liao and Yixiao Sun},
title = {Sieve inference on . . . },
year = {2012}
}
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Abstract
The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a “pre-asymptotic” sieve variance estimator that captures temporal dependence. We construct a “pre-asymptotic” Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled “pre-asymptotic” Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled “pre-asymptotic” Wald test with F critical values
Keyphrases
sieve inference temporal dependence plug-in sieve estimator irregular functionals pre-asymptotic sieve variance estimator general theory nonparametric model series number sieve estimator pre-asymptotic wald statistic accurate inference procedure os-lrv estimator critical value small sample semi nonparametric time series model asymptotic variance run variance asymptotic normality scaled pre-asymptotic wald statistic surprising result orthonormal series root-t estimable pre-asymptotic wald test
