Dependence testing in generalized partially linear regression: asymptotic power of Kendall’s τ
Year: 2026
Type: article
Abstract: In this study, we are motivated to study the asymptotic power of Kendall's τ within the framework of a generalized partially linear regression model, given by) are nonparametric regressors q and e denotes the error term.The model incorporates p unknown parameters b 1 , . . ., b p and an unknown smooth function ϕ(•, . . ., •).Our main objective is to test for dependence between the combined set of regressors S = (X 1 , . . ., X p , V 1 , . . ., V q ) ′ and the error term e.Under the null hypothesis of independence, the general-order differences between observed responses and their estimated counterparts remain independent.To construct an appropriate test, we introduce statistics based on V-statistics, derived from bivariate observations formed using these differences.These statistics act as empirical analogs of Kendall's τ, as originally proposed in Kendall (1938).Additionally, we consider the test statistics based on the nonparametric measures τ * and dCov in analogous manner to carry out a comparative power analysis under a sequence of local alternatives.By specifying different conditional distributions for the error term e, we assess the asymptotic power through the limiting distribution of a non-degenerate V-statistic.For a real dataset, we compare their effectiveness by evaluating p-values and finite sample powers.
Author: Sthitadhi Das
Institution: Brainware University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: University of Burdwan
OpenAlex ID: W7147456248
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