Testing Independence of Covariates and Errors in Non‐parametric Regression. (2nd October 2017)

• Record Type: Journal Article
• Authors: Dhar, Subhra Sankar; Bergsma, Wicher; Dassios, Angelos
• Is Part Of: Scandinavian journal of statistics. Volume 45:Number 3(2018:Sep.)
• Page Start: 421
• Page End: 443
• Publication Date: 2017-10-02
• Subjects: asymptotic power -- contiguous alternatives -- distance covariance -- Kendall's tau -- non‐parametric regression model -- measure of association; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12301
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: Consider a non‐parametric regression model Y = m ( X )+ ϵ, where m is an unknown regression function, Y is a real‐valued response variable, X is a real covariate, and ϵ is the error term. In this article, we extend the usual tests for homoscedasticity by developing consistent tests for independence between X and ϵ . Further, we investigate the local power of the proposed tests using Le Cam's contiguous alternatives. An asymptotic power study under local alternatives along with extensive finite sample simulation study shows that the performance of the new tests is competitive with existing ones. Furthermore, the practicality of the new tests is shown using two real data sets.