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Average Collapsibility of Distribution Dependence and Quantile Regression Coefficients
Author(s) -
VELLAISAMY P.
Publication year - 2012
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/j.1467-9469.2011.00757.x
Subject(s) - mathematics , homogeneity (statistics) , statistics , quantile , conditional probability distribution , marginal distribution , quantile regression , marginal model , random variable , conditional expectation , regression analysis , distribution (mathematics) , econometrics , mathematical analysis
. The Yule–Simpson paradox notes that an association between random variables can be reversed when averaged over a background variable. Cox and Wermuth introduced the concept of distribution dependence between two random variables X and Y , and gave two dependence conditions, each of which guarantees that reversal of qualitatively similar conditional dependences cannot occur after marginalizing over the background variable. Ma, Xie and Geng studied the uniform collapsibility of distribution dependence over a background variable W , under stronger homogeneity condition. Collapsibility ensures that associations are the same for conditional and marginal models. In this article, we use the notion of average collapsibility, which requires only the conditional effects average over the background variable to the corresponding marginal effect and investigate its conditions for distribution dependence and for quantile regression coefficients.