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Activity Number: 329
Type: Invited
Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #318155 View Presentation
Title: An Adaptive-to-Model Test for Parametric Single-Index Errors-in-Covariables Models
Author(s): Lixing Zhu* and Hira L. Koul and Chuan-Long Xie
Companies: Hong Kong Baptist University and Michigan State University and Hong Kong Baptist University
Keywords: Dimension reduction ; errors-in-covariables ; model checking ; adaptive-to-model test

This paper provides some useful tests for fitting a parametric single-index regression model when covariates are measured with error and validation data is available. We propose two tests whose consistency rates do not depend on the dimension of the covariate vector when an adaptive-to-model strategy is applied. One of these tests has a bias term that becomes arbitrarily large with increasing sample size but its asymptotic variance is smaller, and the other is asymptotically unbiased with larger asymptotic variance. Compared with the existing local smoothing tests, the new tests behave like a classical local smoothing test with only one covariate, and still are omnibus against general alternatives. This avoids the difficulty associated with the curse of dimensionality. 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 behavior of these tests. Simulations are conducted to examine the performance in finite sample scenarios.

Authors who are presenting talks have a * after their name.

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