## Electronic Journal of Statistics

### Finite sample behavior of a sieve profile estimator in the single index model

Andreas Andresen

#### Abstract

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.

#### Article information

Source
Electron. J. Statist., Volume 9, Number 2 (2015), 2528-2641.

Dates
First available in Project Euclid: 19 November 2015

https://projecteuclid.org/euclid.ejs/1447943705

Digital Object Identifier
doi:10.1214/15-EJS1079

Mathematical Reviews number (MathSciNet)
MR3425365

Zentralblatt MATH identifier
1326.62046

#### Citation

Andresen, Andreas. Finite sample behavior of a sieve profile estimator in the single index model. Electron. J. Statist. 9 (2015), no. 2, 2528--2641. doi:10.1214/15-EJS1079. https://projecteuclid.org/euclid.ejs/1447943705

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