On a central limit theorem for shrunken weakly dependent random variables

2014/10/01 by Richard C. Bradley, Bradley, Richard C., Zbigniew J. Jurek +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F05 #60G10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1410.0214

openalex publication_date 2014/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A central limit theorem is proved for some strictly stationary sequences of random variables that satisfy certain mixing conditions and are subjected to the "shrinking operators" U_r(x):=[max\|x|-r,0\]⋅ x/|x|, r ≥ 0. For independent, identically distributed random variables, this result was proved earlier by Housworth and Shao.

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• Limit Theorems Under Several Linear Constraints