A Nonparametric Test for Stochastic Dominance Using Total Time on Test Transform

Abstract

SYNOPTIC ABSTRACTThe concept of stochastic dominance has found important applications in the theory and applications of economics and statistics. It refers to a set of relations that may hold between a pair of distributions of random variables. In this article, we present a new definition of stochastic dominance using total time on test transform. The proposed definition based on total time on test is expressed in terms of quantile functions. The total time on test transform of order S is a generalization of the well-known Sth order stochastic dominance. A simple nonparametric test is developed to test the proposed stochastic dominance. It is shown that the distribution of the test statistic is asymptotically normal. Simulation studies are carried out to assess the efficiency of the test. We apply the proposed test to a real-life dataset of personal expenditures.