Multivariate boundary regression models
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In this work, we consider a nonparametric regression model with one-sided errors, multivariate covariates and regression function in a general Hölder class. We work under the assumption of regularly varying independent and identically distributed errors that are also independent of the design points. Following Drees, Neumeyer and Selk (2019), we estimate the regression function, i.e, the upper boundary curve, via minimization of the local integral of a polynomial approximation lying above the data points. The main purpose of this paper is to show the uniform consistency and to provide the rates of convergence of such estimators 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.
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