Rank tests for independence - With a weighted contamination alternative

Two rank tests for independence of bivariate random variables against an al ternative model with weighted contamination are proposed. The model may emp hasize the association of X and Y on items with high ranks in one variable (say X) and generalizes an alternative in Hajek and Sidak (1967). The model may be applied to both complete paired data and paired data which is trunc ated 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 hypot hesis of independence, both rank statistics have limiting normal distributi ons. An application to a data set from a special education program in Taiwa n and a simulation study are presented. We also apply the Shapiro-Francia t est to find the minimum sample sizes for approximate normality of exact dis tributions of the proposed test statistics.