Testing the Conditional Mean Independence for Functional Data

• Activity Number: 297 - Advances in Nonparametric Testing
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Chung Eun Lee* and Xianyang Zhang and Xiaofeng Shao
• Companies: University of Illinois-Urbana Champaign and Texas A&M University and University of Illinois, At Urbana-Champaign
• Keywords: Conditional Mean Test ; Functional Data ; Nonparametric Models ; Wild Bootstrap

Abstract

In this talk, we propose a new nonparametric conditional mean independence test for a response Y and a predictor X where either one can be function-valued. Our test is built on a new metric, the so-called functional martingale difference divergence (FMDD), which fully characterizes the conditional mean dependence between Y and X so it is capable of detecting all types of departure from the null hypothesis of conditional mean independence without imposing any model assumptions. We define unbiased estimator of FMDD by using U-centering approach whose limiting null distribution is nonpivotal. In order to cope with this fact, we adopt the wild bootstrap method to estimate the critical values of our test statistic under the null. Unlike the recent two tests developed by Kokoszka et al (2008) and Patilea et al. (2015), our test does not require dimension reduction thus our test is easy to implement and is less costly in computation. Promising finite sample performance is demonstrated via simulations comparison with two existing tests.