Universität zu Köln

Mueller, Ursula U., Schick, Anton and Wefelmeyer, Wolfgang ORCID: 0000-0003-4814-0160 (2014). Testing for additivity in partially linear regression with possibly missing responses. J. Multivar. Anal., 128. S. 51 - 62. SAN DIEGO: ELSEVIER INC. ISSN 0047-259X

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Abstract

We consider a partially linear regression model with multivariate covariates and with responses that are allowed to be missing at random. This covers the usual settings with fully observed data and the nonparametric regression model as special cases. We first develop a test for additivity of the nonparametric part in the complete data model. The test statistic is based on the difference between two empirical estimators that estimate the errors in two ways: the first uses a local polynomial smoother for the nonparametric part; the second estimates the additive components by a marginal integration estimator derived from the local polynomial smoother. We present a uniform stochastic expansion of the empirical estimator based on the marginal integration estimator, and we derive the asymptotic distribution of the test statistic. The transfer principle of Koul et al. (2012) then allows a direct adaptation of the results to the case when responses are missing at random. We examine the performance of the tests in a small simulation study. (C) 2014 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Mueller, Ursula U. UNSPECIFIED UNSPECIFIED UNSPECIFIED Schick, Anton UNSPECIFIED UNSPECIFIED UNSPECIFIED Wefelmeyer, Wolfgang UNSPECIFIED orcid.org/0000-0003-4814-0160 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-435563
DOI:	10.1016/j.jmva.2014.03.003
Journal or Publication Title:	J. Multivar. Anal.
Volume:	128
Page Range:	S. 51 - 62
Date:	2014
Publisher:	ELSEVIER INC
Place of Publication:	SAN DIEGO
ISSN:	0047-259X
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ERROR DISTRIBUTION FUNCTION; ROOT-N-CONSISTENT; OF-FIT TESTS; NONPARAMETRIC REGRESSION; EFFICIENT ESTIMATION; SERIES ESTIMATORS; PARAMETRIC REGRESSION; CONVERGENCE; RATES; COMPONENTS Multiple languages Statistics & Probability Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/43556