The Quantitative Significance of the Lucas Critique

Doan, Litterman, and Sims (DLS) have suggested using conditional forecasts to do policy analysis with Bayesian vector autoregression (BVAR) models. Their method seems to violate the Lucas critique, which implies that coefficients of a BVAR model will change when there is a change in policy rules. In this article, we attempt to determine whether the Lucas critique is important quantitatively in a BVAR macro model that we construct. We find evidence following two candidate policy rule changes of significant coefficient instability and of a deterioration in the performance of the DLS method.     

Statistics for Quality and Productivity: A New Graduate-Level Statistics Course

The growing popular realization that American product quality and productivity are no longer without challenge for world leadership presents an opportunity for the American statistical community to make stronger contributions to sound industrial practice than it has in the past. Management consultants, such as Deming and Juran, are promoting philosophies that contain strong statistical components and are being heard by top U.S. executives. There are thus growing opportunities for industrial statisticians. Upon reviewing the content of typical graduate-level statistical quality control courses and books in the light of the present situation, we find them to be inadequate and in some cases to suffer from inappropriate emphases. In this article we discuss our perceptions of what is needed in the way of a new graduate-level course in statistics for quality and productivity (SQP). We further offer for discussion a syllabus for such a course (which is a modification of one used at Iowa State in the 1983 spring semester), some comments on how specific topics might be approached, and also a partially annotated list of references for material that we believe belongs in a modern SQP course.     

Resolving the Mixed Models Controversy

Two standard mixed models with interactions are discussed. When each is viewed in the context of superpopulation models, the mixed models controversy is resolved. The tests suggested by the expected mean squares under the constrained-parameters model are correct for testing the main effects and interactions under both the unconstrained-and constrained-parameters models.     

k-POD: A Method for k-Means Clustering of Missing Data

The k-means algorithm is often used in clustering applications but its usage requires a complete data matrix. Missing data, however, are common in many applications. Mainstream approaches to clustering missing data reduce the missing data problem to a complete data formulation through either deletion or imputation but these solutions may incur significant costs. Our k-POD method presents a simple extension of k-means clustering for missing data that works even when the missingness mechanism is unknown, when external information is unavailable, and when there is significant missingness in the data.

[Received November 2014. Revised August 2015.]     

Automatic locally adaptive smoothing for tree-based set estimation

Tree-based methods similar to CART have recently been utilized for problems in which the main goal is to estimate some set of interest. It is often the case that the boundary of the true set is smooth in some sense, however tree-based estimates will not be smooth, as they will be a union of ‘boxes’. We propose a general methodology for smoothing such sets that allows for varying levels of smoothness on the boundary automatically. The method is similar to the idea underlying support vector machines, which is applying a computationally simple technique to data after a non-linear mapping to produce smooth estimates in the original space. In particular, we consider the problem of level-set estimation for regression functions and the dyadic tree-based method of Willett and Nowak [Minimax optimal level-set estimation, IEEE Trans. Image Process. 16 (2007), pp. 2965–2979].     

Performance of the One-Sample Goodness-of-Fit P–P-Plot Length Test

This article studies the performance of the one-sample goodness-of-fit test which is based on the length of the P–P-plot initially introduced in a similar context by Reschenhofer and Bomze (1991 Reschenhofer , E. , Bomze , I. M. ( 1991 ). Length tests for goodness-of-fit . Biometrika 78 : 207 – 216 . [Google Scholar]). The distributional properties of the length test are revised empirically via simulations. In the Monte Carlo power study that follows the length test is shown empirically to have high power under various alternatives considered relative to members of the Cramér–von Mises family of goodness-of-fit tests, and the Kolmogorov–Smirnov test.     

Evaluating the Effective Degrees of Freedom of the Delete-a-Group Jackknife

The delete-a-group jackknife is sometimes used when estimating the variances of statistics based on a large sample. We investigate heavily poststratified estimators for a population mean and a simple regression coefficient, where both full-sample and domain estimates are of interest. The delete-a-group (DAG) jackknife employing 30, 60, and 100 replicates is found to be highly unstable, even for large sample sizes. The empirical degrees of freedom of these DAG jackknives are usually much less than their nominal degrees of freedom. This analysis calls into question whether coverage intervals derived from replication-based variance estimators can be trusted for highly calibrated estimates.