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Consistent specification tests for semiparametric/nonparametric models based on series estimation methods. (English) Zbl 1027.62027
Summary: This paper considers the problem of consistent model specification tests using series estimation methods. The null models we consider 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.

##### MSC:
 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference 62P20 Applications of statistics to economics 62G09 Nonparametric statistical resampling methods
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