Testing conditional quantile independence with functional covariate

Author:

Feng Yongzhen1,Li Jie2ORCID,Song Xiaojun3

Affiliation:

1. Center for Statistical Science and Department of Industrial Engineering, Tsinghua University , Beijing 100084 , China

2. Center for Applied Statistics and School of Statistics, Renmin University of China , Beijing 100872 , China

3. Department of Business Statistics and Econometrics, Guanghua School of Management and Center for Statistical Science, Peking University , Beijing 100871 , China

Abstract

Abstract We propose a new non-parametric conditional independence test for a scalar response and a functional covariate over a continuum of quantile levels. We build a Cramer–von Mises type test statistic based on an empirical process indexed by random projections of the functional covariate, effectively avoiding the “curse of dimensionality” under the projected hypothesis, which is almost surely equivalent to the null hypothesis. The asymptotic null distribution of the proposed test statistic is obtained under some mild assumptions. The asymptotic global and local power properties of our test statistic are then investigated. We specifically demonstrate that the statistic is able to detect a broad class of local alternatives converging to the null at the parametric rate. Additionally, we recommend a simple multiplier bootstrap approach for estimating the critical values. The finite-sample performance of our statistic is examined through several Monte Carlo simulation experiments. Finally, an analysis of an EEG data set is used to show the utility and versatility of our proposed test statistic.

Funder

National Natural Science Foundation of China

Publisher

Oxford University Press (OUP)

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4. Conditional quantile analysis when covariates are functions, with application to growth data;Chen;Journal of the Royal Statistical Society: Series B (Statistical Methodology),2012

5. Robust inference via multiplier bootstrap;Chen;The Annals of Statistics,2020

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