Abstract

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 suggest to use the wild bootstrap method to approximate the critical values of the test. A small Monte Carlo simulation is reported to examine the finite sample performance of the proposed test. We also show

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