Generalized expected value of continuous random variables and its applications

Su Chen

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 20, 4844-4866

Abstract: In this work, we develop a generalized expected value (GE) of a continuous random variable and propose a novel estimate of GE. Asymptotic normality of this estimator (namely “KWA”) is established and a consistent estimate of the asymptotic variance is given. The relationships between KWA and other existing estimators of central tendency such as sample mean, median, trimmed mean and Hodges-Lehmann estimate are studied. The estimator is also applied to construct one-sample hypothesis testings and confidence intervals of locations of any unknown distributions.

Date: 2021
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DOI: 10.1080/03610926.2020.1725823

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