Significance testing in nonparametric regression base on the bootstrap

Wenceslao González-Manteiga
Authors registered in the RePEc Author Service: Miguel A. Delgado ()

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: We propose a test for selecting explanatory variables in nonparametric regression. The test does not need to estimate the conditional expectation function given all the variables but only those which are significant under the null hypothesis. This feature is compntationally convenient and solves, in part, the problem of the "curse of dimensionality" when selecting regressors in a nonparametric context. The proposed test statistic is based on functionals of an empirical process marked by nonparametric residuals. Contiguous alternatives, converging to the null at a rate n-1I2 can be detected. The asymptotic null distribution of the statistic depends on certain features of the data generating process, and asymptotic tests are difficult to implement except in rare circumstances. We justify the consistency of two bootstrap tests easy to implement, which exhibit good level accuracy for fairly small samples, according to the Monte Carlo simulations reported. These results are also applicable to test other interesting restrictions on nonparametric regression curves, like partial linearity and conditional independence.

Keywords: Nonparametric; regression; seleccion; of; variable; higher; order; kermels; marked; empirical; processes; Wild; bootstrap; restrictions; on; nonparametric; curves (search for similar items in EconPapers)
Date: 1998-10
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:6264

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