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Minimax rates of convergence for nonparametric location-Scale models

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  • Zhao, Bingxin
  • Yang, Yuhong

Abstract

This paper studies minimax rates of convergence for nonparametric location-scale models, which include mean, quantile, expectile and momentile regression settings. Under Hellinger differentiability on the error distribution and other mild conditions, we show that the minimax rate of convergence for estimating the regression function under the squared L2 loss is determined by the metric entropy of the nonparametric function class. Different error distributions, including asymmetric Laplace distribution, asymmetric connected double truncated gamma distribution, connected normal-Laplace distribution, Cauchy distribution and asymmetric normal distribution are studied as examples. Applications on low order interaction models and multiple index models are also given.

Suggested Citation

  • Zhao, Bingxin & Yang, Yuhong, 2026. "Minimax rates of convergence for nonparametric location-Scale models," Journal of Econometrics, Elsevier, vol. 254(PB).
    • Handle: RePEc:eee:econom:v:254:y:2026:i:pb:s0304407626000084
    DOI: 10.1016/j.jeconom.2026.106187
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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