Parameter Estimation Through Weighted Least-Squares Rank Regression with Specific Reference to the Weibull and Gumbel Distributions

Probability plots are often used to estimate the parameters of distributions. Using large sample properties of the empirical distribution function and order statistics, weights to stabilize the variance in order to perform weighted least squares regression are derived. Weighted least squares regression is then applied to the estimation of the parameters of the Weibull, and the Gumbel distribution. The weights are independent of the parameters of the distributions considered. Monte Carlo simulation shows that the weighted least-squares estimators outperform the usual least-squares estimators totally, especially in small samples.     

Paired-Samples Tests of Equivalence

Equivalence tests are used when the objective is to find that two or more groups are nearly equivalent on some outcome, such that any difference is inconsequential. Equivalence tests are available for several research designs, however, paired-samples equivalence tests that are accessible and relevant to the research performed by psychologists have been understudied. This study evaluated parametric and nonparametric two one-sided paired-samples equivalence tests and a standardized paired-samples equivalence test developed by Wellek (2003 Wellek , S. (2003). Testing Statistical Hypotheses of Equivalence . New York : Chapman & Hall/CRC. [Google Scholar]). The two one-sided procedures had better Type I error control and greater power than Wellek's test, with the nonparametric procedure having increased power with non normal distributions.     

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.     

The Econometrics of Piecewise-Linear Budget Constraints

In this article maximum likelihood techniques for estimating consumer demand functions when budget constraints are piecewise linear are exposited and surveyed. Consumer demand functions are formally derived under such constraints, and it is shown that the functions are themselves nonlinear as a result. The econometric problems in estimating such functions are exposited, and the importance of the stochastic specification is stressed, in particular the specification of both unobserved heterogeneity of preferences and measurement error. Econometric issues in estimation and testing are discussed, and the results of the studies that have been conducted to date are surveyed.     

Indexing the Federal Tax System: A Cost-of-Living Approach

In this article, we analyze the indexation of federal taxes, using an approach based on cost-of-living measurement. We use our Tax and Price Index methodology and data base to study an indexed system historically, comparing indexation with the Consumer Price Index (CPI) to actual tax policy, a tax system with constant parameters, and an “exact” indexing scheme. We reach three main conclusions: (a) The sequence of tax reductions implemented between 1967 and 1985 have fallen short of mimicking indexation, (b) wealthier households would have benefited relatively more than lower-income households from indexation, and (c) CPI indexation would not have completely eliminated bracket creep.     

Accent on Teaching Materials

This department includes the two sections New Developments in Statistical Computing and Statistical Computing Software Reviews; suitable contents for each of these sections are described under the respective section heading. Articles submitted for the department, outside the two sections, should not be highly technical and should be relevant to the teaching or practice of statistical computing.

An unbiased estimator of e is used to motivate a simple simulation exercise that requires only observations from the distribution uniform on (0, 1). Antithetic variables are introduced and applied to the simulation problem to give a second unbiased estimator of e with reduced variance.     

Detection and Interpretation of a Multivariate Signal Using Combined Charts

A control procedure is presented in this article that is based on jointly using two separate control statistics in the detection and interpretation of signals in a multivariate normal process. The procedure detects the following three situations: (i) a mean vector shift without a shift in the covariance matrix; (ii) a shift in process variation (covariance matrix) without a mean vector shift; and (iii) both a simultaneous shift in the mean vector and covariance matrix as the result of a change in the parameters of some key process variables. It is shown that, following the occurrence of a signal on either of the separate control charts, the values from both of the corresponding signaling statistics can be decomposed into interpretable elements. Viewing the two decompositions together helps one to specifically identify the individual components and associated variables that are being affected. These components may include individual means or variances of the process variables as well as the correlations between or among variables. An industrial data set is used to illustrate the procedure.