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On distance in total variation between image measures

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  • Davydov, Youri

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 ∞).

Suggested Citation

  • Davydov, Youri, 2017. "On distance in total variation between image measures," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 393-400.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:393-400
    DOI: 10.1016/j.spl.2017.06.022
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    References listed on IDEAS

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    1. Nourdin, Ivan & Poly, Guillaume, 2013. "Convergence in total variation on Wiener chaos," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 651-674.
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