STRAP: Smooth Tests for Multivariate Homogeneity using Random Projections*

原文摘要

In this paper, we propose STRAP (Smooth Tests using RAdom Projections), projected smooth tests for the equality of two multivariate distributions. We employ random projections to map the multivariate data into one-dimensional data and transform the projected data via the probability integral transformation. Under the null hypothesis of homogeneity, the transformed data follow the standard uniform distribution, reducing the problem to testing for uniformity. Building on Neyman’s smooth test for uniformity, we show that STRAP is asymptotically {\chi }^{2} distributed under the null hypothesis and has nontrivial power against local alternatives converging to the null at the two-sample rate {[mn/(m+n)]}^{-1/2}, where m and n are the sample sizes. A data-driven procedure is proposed to automatically select the testing order of the proposed test. Moreover, our method is applicable to discrete and heavy-tailed distributions, which is a key advantage over many existing tests. The empirical size and power of STRAP in finite samples are demonstrated through numerical simulations. The advantages of STRAP are further illustrated through an empirical analysis that assesses the effect of pricing on residential gas consumption.

摘要来源：Taylor & Francis · 出版社摘要