Showing papers by "Joseph W. McKean published in 1996"

Rank-Based Analysis of the Heteroscedastic Linear Model

Abstract: Heteroscedasticity often causes problems in the analysis of linear models. Frequently for such cases, scale is a function of the response. Here, for such models, a methodology is presented based on well-known rank-based procedures. The procedure is iterative. Using the residuals from an initial R estimate of the regression coefficients, scale is estimated by inverting a linear rank test for scale. This in turn leads to a weighted R estimate of the regression coefficients and then to a final estimate of scale. Asymptotic linearity results for these estimates are derived, from which their asymptotic distribution is obtained. The weighted R estimate has the same asymptotic distribution as the optimal (known scale) R estimate; hence it is efficiently robust. Consistent estimates of the standard errors of the R estimates of scale and the regression coefficients are determined. Based on these results, a complete inference for the regression coefficients and the scale parameter is realized, including a ...

The Runs Test for Autocorrelated Errors: Unacceptable Properties

Abstract: The runs test is frequently recommended as a method of testing for nonindependent errors in time-series regression models. A Monte Carlo investigation was carried out to evaluate the empirical properties of this test using (a) several intervention and nonintervention regression models, (b) sample sizes ranging from 12 to 100, (c) three levels of o, (d) directional and nondirectional tests, and (e) 19 levels of autocorrelation among the errors. The results indicate that the runs test yields markedly asymmetrical error rates in the two tails and that neither directional nor nondirectional tests are satisfactory with respect to Type I error, even when the ratio of degrees of freedom to sample size is as high as .98. It is recommended that the test generally not be employed in evaluating the independence of the errors in time-series regression models. An expository article on Mood's (1940) runs test was recently published in this journal (Mogull, 1994). It described some of the more popular applications of the test and pointed out the following anomalies in the performance of the one-sample version when there are runs of two: First, departures from randomness are not identified, and, second, power decreases rather than increases with increases in sample size. The purpose of the present article is to describe the problem with employing the runs test as a diagnostic measure in evaluating the assumption of random errors in regression models. Regression models are often a desirable choice for the analysis of timeseries data, especially in the case of small N. Alternative methods of timeseries analysis based on ARIMA models (Box & Jenkins, 1976) and spectral models (e.g., Granger & Hatanaka, 1964; Jenkins & Watts, 1968; Priestley,

An efficient and high breakdown procedure for model criticism

Abstract: Part of a linear model analysis is the examination of the appropriateness of the chosen model. We propose an exploratory model criticism procedure that exposes hidden outliers, clusters of outliers, or underlying curvature by using diagnostics that exploit the differences between an efficient robust fit and a high breakdown fit. Examples illustrate the procedure.

A Monte Carlo study of robust and least squares response surface methods

Abstract: Response surface methodology is useful for exploring a response over a region of factor space and in searching for extrema. Its generality, makes it applicable to a variety of areas. Classical response surface methodology for a continuous response variable is generally based on least squares fitting. The sensitivity of least squares to outlying observations carries over to the surface procedures. To overcome this sensitivity, we propose response surface methodology based on robust procedures for continuous response variables. This robust methodology is analogous to the methodology based on least squares, while being much less sensitive to outlying observations. The results of a Monte Carlo study comparing it and classical surface methodologies for normal and contaminated normal errors are presented. The results show that as the proportion of contamination increases, the robust methodology correctly identifies a higher proportion of extrema than the least squares methods and that the robust estimates of ex...

Tests for the Jackknife Autocorrelation Estimator rQ2

Abstract: Two tests for the jackknife autocorrelation estimator rQ2 are evaluated. It is shown that a test based on the conventional approach for estimating the standard error of a jackknife estimator leads to unacceptable Type I error. A simple alternative approach leads to a muchmore satisfactory test that is recommended for N > 20.