Rank Tests for Independence — with a Weighted Contamination Alternative

Two rank tests for independence of bivariate random variables against an alternative model with weighted contamination are proposed. The model may emphasize the association of X and Y on items with high ranks in one variable (say X) and generalizes an alternative in Hájek and Šidák (1967). The model may be applied to both complete paired data and paired data which is truncated in one variable. We derive the locally most powerful rank (LMPR) test under the alternative setting. The proposed tests turn out to be asymptotic LMPR tests under Logistic and Extreme Value families. Under the null hypothesis of independence, both rank statistics have limiting normal distributions. An application to a data set from a special education program in Taiwan and a simulation study are presented. We also apply the Shapiro-Francia test to find the minimum sample sizes for approximate normality of exact distributions of the proposed test statistics.