Open Access
December 2009 A maximum likelihood method for the incidental parameter problem
Marcelo J. Moreira
Ann. Statist. 37(6A): 3660-3696 (December 2009). DOI: 10.1214/09-AOS688


This paper uses the invariance principle to solve the incidental parameter problem of [Econometrica 16 (1948) 1–32]. We seek group actions that preserve the structural parameter and yield a maximal invariant in the parameter space with fixed dimension. M-estimation from the likelihood of the maximal invariant statistic yields the maximum invariant likelihood estimator (MILE). Consistency of MILE for cases in which the likelihood of the maximal invariant is the product of marginal likelihoods is straightforward. We illustrate this result with a stationary autoregressive model with fixed effects and an agent-specific monotonic transformation model.

Asymptotic properties of MILE, when the likelihood of the maximal invariant does not factorize, remain an open question. We are able to provide consistent, asymptotically normal and efficient results of MILE when invariance yields Wishart distributions. Two examples are an instrumental variable (IV) model and a dynamic panel data model with fixed effects.


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Marcelo J. Moreira. "A maximum likelihood method for the incidental parameter problem." Ann. Statist. 37 (6A) 3660 - 3696, December 2009.


Published: December 2009
First available in Project Euclid: 17 August 2009

zbMATH: 1183.62040
MathSciNet: MR2549574
Digital Object Identifier: 10.1214/09-AOS688

Primary: 60K35 , C13 , C23
Secondary: C30

Keywords: Incidental parameters , Invariance , limits of experiments , maximum likelihood estimator

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6A • December 2009
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