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arXiv · 2105.07406

General order adjusted Edgeworth expansions for generalized $t$-tests

Inna Gerlovina·Alan E. Hubbard
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Abstract

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.

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Inna Gerlovina, Alan E. Hubbard. 2021-05-16. General order adjusted Edgeworth expansions for generalized $t$-tests. https://arxiv.org/abs/2105.07406

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