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Group Invariance, Likelihood Ratio Tests, and the Incidental Parameter Problem in a High-Dimensional Linear Model

Marc Hallin (), Marcelo Moreira () and Alexei Onatski ()

No ECARES 2013-04, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: This paper considers a linear panel data model with reduced rank regressors and interactive fixed effects. The leading example is a factor model where some of the factors are observed, some others not. Invariance considerations yield a maximal invariant statistic whose density does not depend on incidental parameters. It is natural to consider a likelihood ratio test based on the maximal invariant statistic. Its density can be found by using as a prior the unique invariant distribution for the incidental parameters. That invariant distribution is least favorable and leads to minimax optimality properties. Combining the invariant distribution with a prior for the remaining parameters gives a class of admissible tests. A particular choice of distribution yields the spiked covariance model of Johnstone (2001). Numerical simulations suggest that the maximal invariant likelihood ratio test outperforms the standard likelihood ratio test. Tests which are not invariant to data transformations (i) are uniquely represented as randomized tests of the maximal invariant statistic and (ii) do not solve the incidental parameter problem.

Keywords: panel data models; factor model; incidental parameters; invariance; integrated likelihood; minimax; likelihood ratio test (search for similar items in EconPapers)
JEL-codes: C12 C44 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2013-01
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