Estimation and hypotheses testing in boundary regression models

被引:3
|
作者
Drees, Holger [1 ]
Neumeyer, Natalie [1 ]
Selk, Leonie [1 ]
机构
[1] Univ Hamburg, Dept Math, Bundesstr 55, D-20146 Hamburg, Germany
关键词
goodness-of-fit testing; irregular error distribution; one-sided errors; residual empirical distribution function; uniform rates of convergence; NONPARAMETRIC REGRESSION; FRONTIER ESTIMATION; ERROR DISTRIBUTION; KERNEL REGRESSION; BOOTSTRAP; MONOTONE; POINT;
D O I
10.3150/17-BEJ992
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Consider a nonparametric regression model with one-sided errors and regression function in a general Holder class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform rates of convergence for the simple regression estimator as well as for a smooth version. These rates carry over to mean regression models with a symmetric and bounded error distribution. In such a setting, one obtains faster rates for irregular error distributions concentrating sufficient mass near the endpoints than for the usual regular distributions. The results are applied to prove asymptotic root n-equivalence of a residual-based (sequential) empirical distribution function to the (sequential) empirical distribution function of unobserved errors in the case of irregular error distributions. This result is remarkably different from corresponding results in mean regression with regular errors. It can readily be applied to develop goodness-of-fit tests for the error distribution. We present some examples and investigate the small sample performance in a simulation study. We further discuss asymptotically distribution-free hypotheses tests for independence of the error distribution from the points of measurement and for monotonicity of the boundary function as well.
引用
收藏
页码:424 / 463
页数:40
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