Generalized Moment Based Estimation and Inference

We extend the empirical likelihood method of estimation and inference proposed by Owen and others and demonstrate how it may be used in a general linear model context and to mitigate the impact of an ill-conditioned design matrix. A dual loss information theoretic estimating function is used along with extended moment conditions to yield a data based estimator that has the usual consistency and asymptotic normality results. Limiting chi-square distributions may be used to obtain hypothesis test or confidence intervals. The estimator appears to have excellent finite sample properties under a squared error loss measure.