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When there is uncertainty concerning the appropriate statistical model and corresponding estimators and inference methods, we use the Cressie--Read measure of divergence to define a semiparametric estimator, [??]([??]), that combines plausible estimation problems. This estimation procedure identifies, conditional on the data, an optimal combination of competing estimators for the unknown parameters associated with the alternative plausible structural model specifications. The optimization is handled internally and avoids the tuning parameters usually necessary in problems of this type. To illustrate finite sample performance, an extensive sampling experiment is conducted to demonstrate the adaptive nature of the estimator for an array of data sampling specifications. JEL Classification: C10; C24 Keywords: Semiparametric estimation and inference; Empirical likelihood; Convex combination of estimators; Asymptotic and finite sample risk

Asymptotically, semi parametric estimators of the parameters in linear structural models have the same sampling properties. In finite samples the sampling properties of these estimators vary and large biases may result for sample sizes often found in practice. With a goal of improving asymptotic risk performance and finite sample efficiency properties, we investigate the idea of combining correlated structural equation estimators with different finite and asymptotic sampling characteristics. Based on a quadratic loss measure, we present evidence that the finite sample performance of the resulting combination estimator can be notably superior to that of a leading traditional moment based estimator. Keywords: Combined estimators: Quadratic loss; Semiparametric estimation; Data dependent shrinkage; Instrumental variables

In this paper we consider the case of the general linear statistical model, where the stochastic design matrix has the property that its expectation and probability limits with the vector of unobserved disturbances does not equal to a zero vector and moreover, the explanatory and/or instrumental variables are ill-conditioned. In this context, we contemplate generalized moment based estimating functions that may be biased, and for which the corresponding system of moment conditions are overdetermined. To cope with this situation, we propose a new estimator with attractive finite and asymptotic sampling properties and that result in entropic densities on model parameters. MSC: Primary 62E20 JEL classification: C10; C13; C24 Keywords: Method of moments; Generalized method of moments; Empirical likelihood; Semiparametric models; Extended estimating equation; Kullback-Leibler information criterion; Ill-conditioned matrices; Balanced-dual estimating functions

We propose a new formulation of the statistical model and the use of the maximum entropy principle for recovering information when the dependent variable is censored or ordered. This approach makes use of weak sampling assumptions and performs well over a range of non Gaussian error distributions and ill-posed and well-posed problems. Analytical and illustrative Monte Carlo sampling results are presented. Key words: Censored data, Tobit, Ordered multinomial statistical model, Maximum entropy estimator, Cross entropy estimator

Two estimation problems constructed from dynamic discrete time models are examined. One problem concerns noisy state observations in a case where there is nonlinearity between the observation and state equations. In this problem, the goal is to estimate the observation and state equation parameters and the unknown values of the state variable. The other problem concerns a case of linear-quadratic control where the objective is to estimate state equation and objective function parameters. In both cases, a nonlinear inversion procedure is proposed for estimating unknown parameters.

An exact test proposed by Weerahandi (1987) for testing the equality of location vectors under heteroskedasticity is compared with a commonly-used computationally simple asymptotic test. The results from a variety of sampling experiments indicate that in most instances the nominal size of Weerahandi's test (FW) overstates the probability of a Type I error and the nominal size of the asymptotic test (FA) understates the probability of a Type I error. Consequently, without size correction, the probability of a Type II error is less for FA than it is for FW. With size correction the powers of the two tests are virtually identical. Within an estimation context the risk properties of the pre-test estimators generated by FA and FW are compared, and an empirical Bayes estimator is developed within the framework of the more general seemingly unrelated regressions model. Under a squared error loss measure the empirical Bayes estimator is shown to behave in a minimax way.

In this paper we evaluate under a squared error loss measure the risk of a two-stage pre-test estimator (2SPE) for the two-sample problem where there is uncertainty concerning both the equality of the location vectors and the scale parameters. The risk performance of the 2SPE is analytically derived and numerically evaluated and compared with that of other traditional estimators that have been proposed for this statistical model.