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].     

Maximum likelihood estimation of the bimodal failure rate for censored and tied observations

DIMITROV, RACHEV and YAKOVLEV ( 1985 ) have obtained the isotonic maximum likelihood estimator for the bimodal failure rate function. The authors considered only the complete failure time data. The generalization of this estimator for the case of censored and tied observations is now proposed.     

On a statistic useful in dimensionality reduction in multivariable linear stochastic system

In this paper we study the sampling properties of a test statistic which has important applications in the area of linear stochastic control systems with multi-inputs and multi-outputs. The statistic is the ratio of a partial sum of the eigenvalues of a sample covariance matrix and its trace. It turns out that using a method due to Sugiura we may derive a useful approximation for its distribution up to and including terms of order l/n, where n denotes the appropriate size. Numerical illustrations using real data are given.     

Combining Economic Forecasts

A method for combining forecasts may or may not account for dependence and differing precision among forecasts. In this article we test a variety of such methods in the context of combining forecasts of GNP from four major econometric models. The methods include one in which forecasting errors are jointly normally distributed and several variants of this model as well as some simpler procedures and a Bayesian approach with a prior distribution based on exchangeability of forecasters. The results indicate that a simple average, the normal model with an independence assumption, and the Bayesian model perform better than the other approaches that are studied here.     

Normalized Quadratic Systems of Consumer Demand Functions

Empirically estimated demand systems frequently fail to satisfy the appropriate theoretical curvature conditions. We propose and estimate two demand systems for which these conditions can be imposed globally; the first is derived from a normalized quadratic reciprocal indirect utility function and the second is derived from a normalized quadratic expenditure function. The former is flexible if there are no restrictions on its free parameters, but loses flexibility if the curvature conditions need to be imposed. The latter is flexible, in the class of functions satisfying local money metric scaling, even if the curvature conditions need to be imposed.     

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.     

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.