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Model uncertainty is a prominent feature in many applied settings. This is certainty true in the efficiency analysis realm where concerns over the proper distributional specification of the error components of a stochastic frontier model is, generally, still open along with which variables influence inefficiency. Given the concern over the impact that model uncertainty is likely to have on the stochastic frontier model in practice, the present research proposes two distinct model averaging estimators, one which averages over nested classes of inefficiency distributions and another that has the ability to average over distinct distributions of inefficiency. Both of these estimators are shown to produce optimal weights when the aim is to uncover conditional inefficiency at the firm level. We study the finite-sample performance of the model average estimator via Monte Carlo experiments and compare with traditional model averaging estimators based on weights constructed from model selection criteria and present a short empirical application.

This paper considers the post-J test inference in non-nested linear regression models. Post-J test inference means that the inference problem is considered by taking the first stage J test into account. We first propose a post-J test estimator and derive its asymptotic distribution. We then consider the test problem of the unknown parameters, and a Wald statistic based on the post-J test estimator is proposed. A simulation study shows that the proposed Wald statistic works perfectly as well as the two-stage test from the view of the empirical size and power in large-sample cases, and when the sample size is small, it is even better. As a result, the new Wald statistic can be used directly to test the hypotheses on the unknown parameters in non-nested linear regression models.

Most of the literature on clustered data models emphasizes two-level clustering, and within-cluster correlation. While multi-level clustered data models can arise in practice, analysis of multi-level clustered data models poses additional difficulties owing to the existence of error correlations both within and across the clusters. It is perhaps for this reason that existing approaches to multi-level clustered data models have been mostly parametric. The purpose of this paper is to develop a varying-coefficient nonparametric approach to the analysis of three-level clustered data models. Because the nonparametric functions are restricted only to some of the variables, this approach has the appeal of avoiding many of the curse of dimensionality problems commonly associated with other nonparametric methods. By applying an undersmoothing technique, taking into account the correlations within and across clusters, we develop an efficient two-stage local polynomial estimation procedure for the unknown coefficient functions. The large and finite sample properties of the resultant estimators are examined; in particular, we show that the resultant estimators are asymptotically normal, and exhibit considerably smaller asymptotic variability than the traditional local polynomial estimators that neglect the correlations within and among clusters. An application example is presented based on a data set extracted from the World Bank’s STARS database.

We study estimation and inference in a marginal proportional hazards model that can handle (1) linear effects, (2) non-linear effects and (3) interactions between covariates. The model under consideration is an amalgamation of three existing marginal proportional hazards models studied in the literature. Developing an estimation and inference procedure with desirable properties for the amalgamated model is rather challenging due to the co-existence of all three effects listed above. Much of the existing literature has avoided the problem by considering narrow versions of the model. The object of this paper is to show that an estimation and inference procedure that accommodates all three effects is within reach. We present a profile partial-likelihood approach for estimating the unknowns in the amalgamated model with the resultant estimators of the unknown parameters being root- $$n$$ consistent and the estimated functions achieving optimal convergence rates. Asymptotic normality is also established for the estimators.

This paper compares the Stein and the usual estimators of the error variance under the Pitman nearness (PN) criterion in a regression model which is mis-specified due to missing relevant explanatory variables. The exact expression of the PN-probability is derived and numerically evaluated. Contrary to the well-known result under mean squared errors (MSE), with the PN criterion the Stein variance estimator is uniformly dominated by the usual estimator when no relevant variables are excluded from the model. With an increased degree of model mis-specification, neither estimator strictly dominates the other.

We consider the estimation of the error variance of a linear regression model where prior information is available in the form of an (uncertain) inequality constraint on the coefficients. Previous studies on this and other related problems use the squared error loss in comparing estimator’s performance. Here, by adopting the asymmetric LINEX loss function, we derive and numerically evaluate the exact risks of the inequality constrained estimator and the inequality pre-test estimator which results after a preliminary test for an inequality constraint on the coefficients. The risks based on squared error loss are special cases of our results, and we draw appropriate comparisons.

There is a good deal of literature that investigates the properties of various operational variants of Theil's (1971, Principles of Econometrics, Wiley, New York) minimum mean squared error estimator. It is interesting that virtually all of the existing analysis to date is based on the premise that the model's disturbances are i.i.d., an assumption which is not satisfied in many practical situations. In this paper, we consider a model with non-spherical errors and derive the asymptotic distribution, bias and mean squared error of a general class of feasible minimum mean squared error estimators. A Monte-Carlo experiment is conducted to examine the performance of this class of estimators in finite samples.

This paper considers simultaneous estimation of means from several strata under error-in-variables superpopulation models. Necessary and sufficient conditions for an estimator to be admissible in the class of linear estimators are obtained.

This article considers Bayesian inference in the interval constrained normal linear regression model. Whereas much of the previous literature has concentrated on the case where the prior constraint is correctly specified, our framework explicitly allows for the possibility of an invalid constraint. We adopt a non-informative prior and uncertainty concerning the interval restriction is represented by two prior odds ratios. The sampling theoretic risk of the resulting Bayesian interval pre-test estimator is derived, illustrated and explored.

We consider a bivariate normal linear regression model with an inequality restriction imposed on one of the regression coefficients. The exact analytical expressions for the density and distribution functions of the inequality constrained and pre-test estimators are derived and numerically evaluated. The implications of using the inequality constrained and pre-test estimators in confidence interval construction are also discussed and explored.