2021/05/16 by Inna Gerlovina, Alan E. Hubbard, Gerlovina, Inna +1
Mathematics · #41A60 #60E10 #68W30 #FOS: Mathematics #Primary 62E20 #Statistics Theory (math.ST) #math.ST #msc:41A60 #msc:60E10 #msc:60F05 #msc:62E20 #msc:68W30 #secondary 60F05 #stat.TH
paper · pdf · doi:10.48550/arxiv.2105.07406
22 pages, 3 figures, 2 tables
arxiv created 2021/05/16 · arxiv updated 2021/05/18
We develop generalized approach to obtaining Edgeworth expansions for t-statistics of an arbitrary order using computer algebra and combinatorial algorithms. To incorporate various versions of mean-based statistics, we introduce Adjusted Edgeworth expansions that allow polynomials in the terms to depend on a sample size in a specific way and prove their validity. Provided results up to 5th order include one and two-sample ordinary t-statistics with biased and unbiased variance estimators, Welch t-test, and moderated t-statistics based on empirical Bayes method, as well as general results for any statistic with available moments of the sampling distribution. These results are included in a software package that aims to reach a broad community of researchers and serve to improve inference in a wide variety of analytical procedures; practical considerations of using such expansions are discussed.