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Multivariate boundary regression models

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  • Leonie Selk
  • Charles Tillier
  • Orlando Marigliano

Abstract

In this work, we consider a multivariate regression model with one‐sided errors. We assume for the regression function to lie in a general Hölder class and estimate it via a nonparametric local polynomial approach that consists of minimization of the local integral of a polynomial approximation lying above the data points. While the consideration of multivariate covariates offers an undeniable opportunity from an application‐oriented standpoint, it requires a new method of proof to replace the established ones for the univariate case. The main purpose of this paper is to show the uniform consistency and to provide the rates of convergence of the considered nonparametric estimator for both multivariate random covariates and multivariate deterministic design points. To demonstrate the performance of the estimators, the small sample behavior is investigated in a simulation study in dimension two and three.

Suggested Citation

  • Leonie Selk & Charles Tillier & Orlando Marigliano, 2022. "Multivariate boundary regression models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 400-426, March.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:1:p:400-426
    DOI: 10.1111/sjos.12519
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    1. Onizuka, Takahiro & Iwashige, Fumiya & Hashimoto, Shintaro, 2024. "Bayesian boundary trend filtering," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).

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