A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects

Wang, Haiyan and Tolos, Siti Marponga and Wang, Suojin (2010) A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects. The Canadian Journal of Statistics, 38 (3). pp. 408-433. ISSN 0319-5724 (P), 1708-945X (O)

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Abstract

In this paper,we present a test of independence between the response variable, which can be discrete or continuous, and a continuous covariate after adjusting for heteroscedastic treatment effects. The method involves first augmenting each pair of the data for all treatments with a fixed number of nearest neighbours as pseudo-replicates. Then a test statistic is constructed by taking the difference of two quadratic forms. The statistic is equivalent to the average lagged correlations between the response and nearest neighbour local estimates of the conditional mean of response given the covariate for each treatment group. This approach effectively eliminates the need to estimate the nonlinear regression function. The asymptotic distribution of the proposed test statistic is obtained under the null and local alternatives. Although using a fixed number of nearest neighbours pose significant difficulty in the inference compared to that allowing the number of nearest neighbours to go to infinity, the parametric standardizing rate for our test statistics is obtained. Numerical studies show that the new test procedure has robust power to detect nonlinear dependency in the presence of outliers that might result from highly skewed distributions.

Item Type:	Article (Journal)
Additional Information:	6651/5420
Uncontrolled Keywords:	Dependency measure; hypothesis testing; k-nearest neighbours; copula MSC 2000: Primary 62G10; secondary 62J02.
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Siti Marponga Tolos
Date Deposited:	22 Nov 2011 09:27
Last Modified:	07 Dec 2011 16:43
URI:	http://irep.iium.edu.my/id/eprint/5420

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