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CONSISTENCY AND ASYMPTOTIC NORMALITY OF SIEVE ML ESTIMATORS UNDER LOW-LEVEL CONDITIONS

Published online by Cambridge University Press:  11 April 2014

Herman J. Bierens
Herman J. Bierens*
Affiliation:
Pennsylvania State University
*
*Address correspondence to Herman J. Bierens, Professor Emeritus of Economics, Pennsylvania State University, University Park, PA 16802; e-mail: hbierens@psu.edu.
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Abstract

This paper considers sieve maximum likelihood estimation of seminonparametric (SNP) models with an unknown density function as non-Euclidean parameter, next to a finite-dimensional parameter vector. The density function involved is modeled via an infinite series expansion, so that the actual parameter space is infinite-dimensional. It will be shown that under low-level conditions the sieve estimators of these parameters are consistent, and the estimators of the Euclidean parameters are $\sqrt N$ asymptotically normal, given a random sample of size N. The latter result is derived in a different way than in the sieve estimation literature. It appears that this asymptotic normality result is in essence the same as for the finite dimensional case. This approach is motivated and illustrated by an SNP discrete choice model.

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ARTICLES
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Econometric Theory , Volume 30 , Issue 5 , October 2014 , pp. 1021 - 1076
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Copyright © Cambridge University Press 2014 

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