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Testing Independence of Covariates and Errors in Non‐parametric Regression
Author(s) -
Dhar Subhra Sankar,
Bergsma Wicher,
Dassios Angelos
Publication year - 2018
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12301
Subject(s) - homoscedasticity , covariate , mathematics , statistics , independence (probability theory) , regression analysis , parametric statistics , econometrics , regression , power function , term (time) , heteroscedasticity , mathematical analysis , physics , quantum mechanics
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.