On bootstrap consistency of MAVE for single index models

Abstract

This paper concerns the bootstrap consistency of the minimum average variance estimation (MAVE) method for the single index model. This paper shows that the conditional wild bootstrap estimator of the parameter index shares the same asymptotic covariance of the original MAVE estimator. Thus, the asymptotic distribution can be accurately estimated by the proposed wild bootstrap method. As an application of this method, this paper proposes a conditional Wald type test for the parameter index. It will be shown by simulations that the conditional bootstrap based test is more powerful than the test based on the traditional plug-in covariance estimator. A real data analysis is also provided to demonstrate the effectiveness of the bootstrap method.