Semi-parametric transformation boundary regression models

Natalie Neumeyer (), Leonie Selk () and Charles Tillier ()
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Natalie Neumeyer: University of Hamburg
Leonie Selk: University of Hamburg
Charles Tillier: University of Hamburg

Annals of the Institute of Statistical Mathematics, 2020, vol. 72, issue 6, No 1, 1287-1315

Abstract: Abstract In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. In view of estimating the transformation parameter, we use a minimum distance approach and show the uniform consistency of the estimator under mild conditions. The boundary curve, i.e., the regression function, is estimated applying a smoothed version of a local constant approximation for which we also prove the uniform consistency. We deal with both cases of random covariates and deterministic (fixed) design points. To highlight the applicability of the procedures and to demonstrate their performance, the small sample behavior is investigated in a simulation study using the so-called Yeo–Johnson transformations.

Keywords: Box–Cox transformations; Frontier estimation; Minimum distance estimation; Local constant approximation; Boundary models; Nonparametric regression; Yeo–Johnson transformations (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10463-019-00731-5

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