Testing Additivity by Kernel-Based Methods: What Is a Reasonable Test?

Dette, Holger; Wilkau, Carsten von Lieres und

doi:10.2307/3318732

Cited by 18 publications

(35 citation statements)

References 15 publications

(18 reference statements)

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“…See [22][23][24][25][26] and the references therein. The work on the generalized likelihood ratio test [24] offers light into nonparametric inference, based on function estimation under nonparametric models, using the quadratic loss function as the error measure.…”

Section: Discussionmentioning

confidence: 99%

Robust-BD Estimation and Inference for General Partially Linear Models

Zhang

2017

Entropy

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Abstract:The classical quadratic loss for the partially linear model (PLM) and the likelihood function for the generalized PLM are not resistant to outliers. This inspires us to propose a class of "robust-Bregman divergence (BD)" estimators of both the parametric and nonparametric components in the general partially linear model (GPLM), which allows the distribution of the response variable to be partially specified, without being fully known. Using the local-polynomial function estimation method, we propose a computationally-efficient procedure for obtaining "robust-BD" estimators and establish the consistency and asymptotic normality of the "robust-BD" estimator of the parametric component β o . For inference procedures of β o in the GPLM, we show that the Wald-type test statistic W n constructed from the "robust-BD" estimators is asymptotically distribution free under the null, whereas the likelihood ratio-type test statistic Λ n is not. This provides an insight into the distinction from the asymptotic equivalence (Fan and Huang 2005) between W n and Λ n in the PLM constructed from profile least-squares estimators using the non-robust quadratic loss. Numerical examples illustrate the computational effectiveness of the proposed "robust-BD" estimators and robust Wald-type test in the appearance of outlying observations.

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Section: Discussionmentioning

confidence: 99%

Robust-BD Estimation and Inference for General Partially Linear Models

Zhang

2017

Entropy

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“…The norm comparison is provided in Lemma 2. Its proof can be found in Dette and von Lieres und Wilkau (2001).…”

Section: Relative Efficiencymentioning

confidence: 99%

A power comparison between nonparametric regression tests

Zhang

Dette

2004

Statistics & Probability Letters

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In this paper, we consider three major types of nonparametric regression tests that are based on kernel and local polynomial smoothing techniques. Their asymptotic power comparisons are established systematically under the fixed and contiguous alternatives, and are also illustrated through non-asymptotic investigations and finite-sample simulation studies.MSC: primary 62G10; secondary 62G05, 62G20

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“…Although early work dates back to Tukey (1949), it is only recently that the problem of testing for additivity has been of real interest. We refer to Barry (1993), Eubank et al (1995), Gozalo and Linton (2001), Dette and Derbort (2001), Dette and Wilkau (2001), Derbort et al (2002), Sperlich et al (2002), Li et al (2003), De Canditiis and Sapatinas (2004) and Dette et al (2005) for various approaches to testing for additivity in the nonparametric regression models. Despite a growing number of works, almost none of them investigated the optimality of the proposed additivity tests.…”

Section: Introductionmentioning

confidence: 99%