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

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 n...

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Main Authors:	Wang, Haiyan, Tolos, Siti Marponga, Wang, Suojin
Format:	Article
Language:	English
Published:	Statistical Society of Canada 2010
Subjects:	Q Science (General) QA Mathematics
Online Access:	http://irep.iium.edu.my/5420/ http://irep.iium.edu.my/5420/ http://irep.iium.edu.my/5420/ http://irep.iium.edu.my/5420/1/Test.of.independence.Wang.Tolos.Wang.cjs.pdf

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spelling	iium-54202011-12-07T08:43:24Z http://irep.iium.edu.my/5420/ A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects Wang, Haiyan Tolos, Siti Marponga Wang, Suojin Q Science (General) QA Mathematics 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. Statistical Society of Canada 2010-09 Article PeerReviewed application/pdf en http://irep.iium.edu.my/5420/1/Test.of.independence.Wang.Tolos.Wang.cjs.pdf 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) http://onlinelibrary.wiley.com/doi/10.1002/cjs.10068/abstract 10.1002/cjs.10068
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	Q Science (General) QA Mathematics
spellingShingle	Q Science (General) QA Mathematics Wang, Haiyan Tolos, Siti Marponga Wang, Suojin A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects
description	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.
format	Article
author	Wang, Haiyan Tolos, Siti Marponga Wang, Suojin
author_facet	Wang, Haiyan Tolos, Siti Marponga Wang, Suojin
author_sort	Wang, Haiyan
title	A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects
title_short	A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects
title_full	A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects
title_fullStr	A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects
title_full_unstemmed	A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects
title_sort	distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects
publisher	Statistical Society of Canada
publishDate	2010
url	http://irep.iium.edu.my/5420/ http://irep.iium.edu.my/5420/ http://irep.iium.edu.my/5420/ http://irep.iium.edu.my/5420/1/Test.of.independence.Wang.Tolos.Wang.cjs.pdf
first_indexed	2023-09-18T20:14:01Z
last_indexed	2023-09-18T20:14:01Z
_version_	1777407666823364608

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

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