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Consistent specification tests for semiparametric/nonparametric models based on series estimation methods
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DOI：10.1016/S0304-4076(02)00198-7.png)
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Abstract
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This paper considers the problem of consistent model specification tests using series estimation methods. The null models we consider in this paper all contain some nonparametric components. A leading case we consider is to test for an additive partially linear model. The null distribution of the test statistic is derived using a central limit theorem for Hilbert-valued random arrays. The test statistic is shown to be able to detect local alternatives that approach the null models at the order of O-p(n(-1/2)). We show that the wild bootstrap method can be used to approximate the null distribution of the test statistic. A small Monte Carlo simulation is reported to examine the finite sample performance of the proposed test. We also show that the proposed test can be easily modified to obtain series-based consistent tests for other semiparametric/nonparametric models. (C) 2002 Elsevier Science B.V. All rights reserved.
Keywords:
consistent tests
semiparametric models
series estimation
wild bootstrap
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