Scalable Semiparametric Inference for the Means of Heavy-tailed Distributions

Hedibert Freitas Lopes, Matthew Taddy and Matthew Gardner

A chapter in Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B, 2019, vol. 40B, pp 141-156 from Emerald Publishing Ltd

Abstract: Abstract Heavy-tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with internet transaction datasets, and machine learners often analyze such data without considering the biases and risks associated with the misuse of standard tools. This chapter outlines a procedure for inference about the mean of a (possibly conditional) heavy-tailed distribution that combines nonparametric analysis for the bulk of the support with Bayesian parametric modeling – motivated from extreme value theory – for the heavy tail. The procedure is fast and massively scalable. The work should find application in settings wherever correct inference is important and reward tails are heavy; we illustrate the framework in causal inference for A/B experiments involving hundreds of millions of users of eBay.com.

Date: 2019
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