An Adaptive-to-Model Test for Parametric Single-Index Errors-in-Variables Models

Abstract

This paper provides a useful test for parametric single-index regression models when covariates are measured with error and validation data is available. The proposed test is asymptotically unbiased and its consistency rate does not depend on the dimension of the covariate vector. Compared with the existing local smoothing tests, the new test behaves like a classical local smoothing test with only one covariate, and still is omnibus against general alternatives. This suggests that the proposed test has potential for alleviating the difficulty associated with the curse of dimensionality in this field. Further, a systematic study is conducted to give an insight on the effect of the values of the ratio between the sample size and the size of validation data on the asymptotic behaviour of these tests. Simulations are conducted to examine the performance in several finite sample scenarios.