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Coordinate-Based Empirical Likelihood-Like Estimation in III-Conditioned Inverse Problems

Ron Mittelhammer, George Judge, Marco van Akkeren and N. Scott Cardell
Journal of the American Statistical Association
Vol. 97, No. 460 (Dec., 2002), pp. 1108-1121
Stable URL: http://www.jstor.org/stable/3085835
Page Count: 14
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Coordinate-Based Empirical Likelihood-Like Estimation in III-Conditioned Inverse Problems
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Abstract

In the context of a semiparametric regression model with underlying probability distribution unspecified, an extremum estimator formulation is proposed that makes use of empirical likelihood and information theoretic estimation and inference concepts to mitigate the problem of an ill-conditioned design matrix. A squared error loss measure is used to assess estimator performance in finite samples. In large samples, the estimator can be designed to be consistent and asymptotically normal, so that limiting chi-squared distributions provide a basis for hypothesis tests and confidence intervals. Empirical risk results based on a large-scale Monte Carlo sampling experiment suggest that the estimator has, relative to traditional competitors, superior finite-sample properties under a squared error loss measure when the design matrix is ill-conditioned.

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