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2015 Finite sample behavior of a sieve profile estimator in the single index model
Andreas Andresen
Electron. J. Statist. 9(2): 2528-2641 (2015). DOI: 10.1214/15-EJS1079


We apply the results of Andresen et. al. (2014) on finite sample properties of sieve M-estimators and Andresen et. al. (2015) on the convergence of an alternating maximization procedure to analyse a sieve profile maximization estimator in the single index model with linear index function. The link function is approximated with $C^{3}$-Daubechies-wavelets with compact support. We derive results like Wilks phenomenon and Fisher Theorem in a finite sample setup even when the model is miss-specified. Furthermore we show that an alternating maximization procedure converges to the global maximizer and we assess the performance of Friedman’s projection pursuit procedure. The approach is based on showing that the conditions of Andresen et. al. (2014) and (2015) can be satisfied under a set of mild regularity and moment conditions on the link function, the regressors and the additive noise. The results allow to construct non-asymptotic confidence sets and to derive asymptotic bounds for the estimator as corollaries.


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Andreas Andresen. "Finite sample behavior of a sieve profile estimator in the single index model." Electron. J. Statist. 9 (2) 2528 - 2641, 2015.


Received: 1 April 2015; Published: 2015
First available in Project Euclid: 19 November 2015

zbMATH: 1326.62046
MathSciNet: MR3425365
Digital Object Identifier: 10.1214/15-EJS1079

Primary: 62F10
Secondary: 62F25 , 62H12 , 62J12

Keywords: alternating maximization , alternating minimization , Profile estimator , projection pursuit procedure , sieve , single index

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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