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Asymptotic normality of spline estimator when the errors are a linear stationary process 

Authors: Benoicirct Truong-Van a; Noëlle Bru b
Affiliations:   a Lahomtoire de Statistique et Pmbabiliteacutes, Universiteacute Paul Sabatier, Toulouse, France
b Laboratoire de Statistique et d'Analyse des Donneacutees, Universiteacute Pierre Mendeacutes, Grenoble, France
DOI: 10.1080/10485250108832875
Publication Frequency: 8 issues per year
Published in: journal Journal of Nonparametric Statistics, Volume 13, Issue 5 2001 , pages 741 - 761
Formats available: PDF (English)
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Abstract

Smoothing splines are considered for estimating an unknown regular function when the errors in the observations are dependent This dependence is modelled here by assuming that the errors form a linear stationary process defined over some sequence of martingale differences. Some statistical properties of the smoothing spline estimator under consideration are studied and mainly its asymptotic normality is established
Keywords: Spline regression; Martingale differences; Linear stationary process; Asymptotic normality
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