Generalized Point Estimation with Application to Small Response Estimation

Motivated by a number of drawbacks of classical methods of point estimation, we generalize the definitions of point estimation, and address such notions as unbiasedness and estimation under constraints. The utility of the extension is shown by deriving more reliable estimates for small coefficients of regression models, and for variance components and random effects of mixed models. The extension is in the spirit of generalized confidence intervals introduced by Weerahandi (1993 Weerahandi , S. ( 1993 ). Generalized confidence intervals . J. Amer. Statist. Assoc. 88 : 899 – 905 .Taylor & Francis Online], Web of Science ®] , Google Scholar]) and should encourage much needed further research in point estimation in unbalanced models, multi-variate models, non normal models, and nonlinear models.