报告题目：STRAP: Smooth Tests for Multivariate Homogeneity using Random Projections
报告人：宋晓军
时间：2026年1月8日15:00-16:00
地点：西安交通大学创新港涵英楼8121会议室
报告人简介：
宋晓军，北京大学光华管理学院商务统计与经济计量系副教授，博士生导师，西班牙马德里卡洛斯三世大学经济学博士。主要研究兴趣是理论计量经济学，包括非参数/半参数方法，假设检验和自助法，以及计量经济学的应用等。论文发表在Journal of Econometrics，Management Science，Econometric Reviews, Econometric Theory, Journal of Applied Econometrics, Journal of Business & Economic Statistics, Oxford Bulletin of Economics and Statistics等国际期刊。主持和参加自然科学基金面上项目和重点项目等。获得北京大学优秀班主任、北京大学优秀博士学位论文指导教师、北京大学蔡元培美育奖教金等荣誉。自2020年1月起，担任Economic Modelling副主编。
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-square 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. We extend the methodology to the fixed-K setting, where the number of projection directions is held constant, and the paired-sample case, where observations are dependent and collected in matched pairs. For both scenarios, we propose adjusted test statistics that retain the desirable asymptotic properties. 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, which assesses the pricing effect on residential gas consumption.
