An Extended Approach to Test of Independence between Error and Covariates under Nonparametric Regression Model
Keywords:Kendall’s tau, measures of association, asymptotic power, contiguous alternative, nonparametric regression model
In 2014, Bergsma et al. (2014) proposed a generalized measure of association as an extension
of widely used Kendall’s . Later, in testing of independence between error and covariate, under
nonparametric regression model with unknown regression function and observation error test statistic tailored on was suggested by Dhar et al. (2018). In this article, we develop a test, constructed on further extension of considering the ordered and the third order difference of 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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