An Extended Approach to Test of Independence between Error and Covariates under Nonparametric Regression Model

Authors

  • Sthitadhi Das Department of Statistics, Institute of Sciences, Visva Bharati, Santiniketan, India
  • Soutik Halder Department of Statistics, Institute of Sciences, Visva Bharati, Santiniketan, India
  • Saran Ishika Maiti Department of Statistics, Institute of Sciences, Visva Bharati, Santiniketan, India

Keywords:

Kendall’s tau, measures of association, asymptotic power, contiguous alternative, nonparametric regression model

Abstract

In 2014, Bergsma et al. (2014) proposed a generalized measure of association gif.latex?\tau&space;^*   as an extension
of widely used Kendall’s  gif.latex?\tau.   Later, in testing of independence between error and covariate, under
nonparametric regression model  gif.latex?Y=m(x)+\varepsilon,  with unknown regression function gif.latex?m  and observation error  gif.latex?\varepsilon,   test statistic tailored on  gif.latex?\tau&space;^*   was suggested by Dhar et al. (2018). In this article, we develop a test, constructed on further extension of  gif.latex?\tau&space;^*,  considering the ordered gif.latex?X  and the third order difference of gif.latex?Y  with an motive to address the same issue of independence. We deduce the asymptotic distributions of test statistics using the theory of degenerate U-statistics. Moreover, we unravel the
power of the proposed tests using Le Cam’s concept of contiguous alternatives. A couple of simulated examples on normal and non normal distribution are furnished. Also, the performance of the test statistics is honed through a real data analysis.








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Published

2022-12-29

How to Cite

Das, S. ., Halder , S. ., & Ishika Maiti, S. . (2022). An Extended Approach to Test of Independence between Error and Covariates under Nonparametric Regression Model. Thailand Statistician, 21(1), 19–36. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/248015

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Articles