Extended rank analysis of covariance adjusting for local correlations

An implicit assumption in the classical analysis of covariance is that the relationship between the response variable Y and the covariable X is consistent across the support of X. This may not hold in general if the strength of the relationship between Y and X varies in different regions of the covariate space [Doksum, K., Blyth, S., Bradlow, E., Meng, X.-L., Zhao, H., 1994. Correlation curves as local measures of variance explained by regression. J. Amer. Statist. Assoc. 89 (426), 571–582]. In this paper, to cope with heterocorrelaticity nonparametrically, we propose an extended rank analysis of covariance by adjusting local tolerances and dividing the support of X into disjoint subintervals with substantial different correlations between Y and X. The results showed that the proposed method was flexible in model error distributions as well as changing local correlations between Y and X, while retaining relatively well empirical power in simulations.