Asymptotic Power of a Spearman’s Rank Correlation Coefficient in Generalized Partially Linear Logistic Regression

Abstract

This paper investigates the asymptotic power of a Spearman’s rank correlation-based test for assessing independence between the joint regressors and the error term in a generalized partially linear logistic regression model. The proposed test statistic is constructed using general order differences of the observed binary responses and their fitted probabilities, leveraging the property that independence between joint covariates and the error term implies asymptotic independence between these order differences under mild regularity conditions. We introduce a sequence of contiguous alternatives to derive the limiting distribution of the test and to compute its asymptotic power. Simulation studies demonstrate strong finite-sample performance and confirm the theoretical power results. A real-data application further highlights the practical usefulness of the proposed method.