On distance in total variation between image measures

Youri Davydov

Statistics & Probability Letters, 2017, vol. 129, issue C, 393-400

Abstract: We are interested in the estimation of the distance in total variation Δ≔‖Pf(X)−Pg(X)‖varbetween distributions of random variables f(X) and g(X) in terms of proximity of f and g. We propose a simple general method of estimating Δ. For Gaussian and trigonometrical polynomials it gives an asymptotically optimal result (when the degree tends to ∞).

Keywords: Total variation distance; Image-measures; Gaussian polynomials; Nikol’ski–Besov class (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.06.022

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