This paper discussed “Invidious Comparisons: Ranking and Selection as Compound Decisions” by Jiaying Gu and Roger Koenker.

This paper develops asymptotic optimality theory for statistical treatment rules in smooth parametric and semiparametric models. Manski (2000, 2002, 2004) and Dehejia (2005) have argued that the problem of choosing treatments to maximize social welfare is distinct from the point estimation and hypothesis testing problems usually considered in the treatment effects literature, and advocate formal analysis of decision procedures that map empirical data into treatment choices. We develop large-sample approximations to statistical treatment assignment problems using the limits of experiments framework. We then consider some different loss functions and derive treatment assignment rules that are asymptotically optimal under average and minmax risk criteria.

In certain auction, search, and related models, the boundary of the support of the observed data depends on some of the parameters of interest. For such nonregular models, standard asymptotic distribution theory does not apply. Previous work has focused on characterizing the nonstandard limiting distributions of particular estimators in these models. In contrast, we study the problem of constructing efficient point estimators. We show that the maximum likelihood estimator is generally inefficient, but that the Bayes estimator is efficient according to the local asymptotic minmax criterion for conventional loss functions. We provide intuition for this result using Le Cam's limits of experiments framework. Copyright The Econometric Society 2003.

We consider forecasting with uncertainty about the choice of predictor variables. The researcher wants to select a model, estimate the parameters, and use this for forecasting. We investigate the dis-tributional properties of a number of different schemes for model choice and parameter estimation: in-sample model selection using the Akaike information criterion, out-of-sample model selection, and splitting the data into subsamples for model selection and parameter estimation. Using a weak-predictor local asymptotic scheme, we provide a representation result that facilitates comparison of the distributional properties of the procedures and their associated forecast risks. We develop a sim-ulation procedure that improves the accuracy of the out-of-sample and split-sample methods uni-formly over the local parameter space. We also examine how bootstrap aggregation (bagging) affects the local asymptotic risk of the estimators and their associated forecasts. Numerically, we find that for many values of the local parameter, the out-of-sample and split-sample schemes perform poorly if implemented in the conventional way. But they perform well, if implemented in conjunction with our risk-reduction method or bagging.

We examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the existence of unbiased and regular estimators, we show that if the target object is not differentiable in the parameters of the data distribution, there exist no estimator sequences that are locally asymptotically unbiased or α-quantile unbiased. This places strong limits on estimators, bias correction methods, and inference procedures, and provides motivation for considering other criteria for evaluating estimators and inference procedures, such as local asymptotic minimaxity and one-sided quantile unbiasedness.

We consider estimation of population averages when data are missing at random. If some cells contain few observations, there can be substantial gains from imposing parametric restrictions on the cell means, but there is also a danger of misspecification. We develop a simple empirical Bayes estimator, which combines parametric and unadjusted estimates of cell means in a data-driven way. We also consider ways to use knowledge of the form of the propensity score to increase robustness. We develop an empirical Bayes extension of a double robust estimator. In a small simulation study, the empirical Bayes estimators perform well. They are similar to fully nonparametric methods and robust to misspecification when cells are moderate to large in size, and when cells are small they maintain the benefits of parametric methods and can have lower sampling variance.

We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is exogenous or unconfounded, that is, independent of the potential outcomes given covariates, biases associated with simple treatment-control average comparisons can be removed by adjusting for differences in the covariates. Rosenbaum and Rubin (1983) show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates. Although adjusting for differences in the propensity score removes all the bias, this can come at the expense of efficiency, as shown by Hahn (1998), Heckman, Ichimura, and Todd (1998), and Robins, Mark, and Newey (1992). We show that weighting by the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to an efficient estimate of the average treatment effect. We provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score.