# A maximum likelihood method for the incidental parameter problem - Mathematics > Statistics Theory

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Abstract: This paper uses the invariance principle to solve the incidental parameterproblem of Econometrica 16 1948 1-32. We seek group actions that preservethe structural parameter and yield a maximal invariant in the parameter spacewith fixed dimension. M-estimation from the likelihood of the maximal invariantstatistic yields the maximum invariant likelihood estimator MILE. Consistencyof MILE for cases in which the likelihood of the maximal invariant is theproduct of marginal likelihoods is straightforward. We illustrate this resultwith a stationary autoregressive model with fixed effects and an agent-specificmonotonic transformation model. Asymptotic properties of MILE, when thelikelihood of the maximal invariant does not factorize, remain an openquestion. We are able to provide consistent, asymptotically normal andefficient results of MILE when invariance yields Wishart distributions. Twoexamples are an instrumental variable IV model and a dynamic panel data modelwith fixed effects.

Author: ** Marcelo J. Moreira**

Source: https://arxiv.org/