AMEMIYA'S FORM OF THE WEIGHTED LEAST SQUARES ESTIMATOR

Amemiya's estimator is a weighted least squares estimator of the regression coefficients in a linear model with heteroscedastic errors. It is attractive because the heteroscedasticity is not parametrized and the weights (which depend on the error covariance matrix) are estimated nonparametrically. This paper derives an asymptotic expansion for Amemiya's form of the weighted least squares estimator, and uses it to discuss the effects of estimating the weights, of the number of iterations, and of the choice of the initial estimate. The paper also discusses the special case of normally distributed errors and clarifies the particular consequences of assuming normality.     

Metropolitan retail nucleation

We argue that U.S. metropolitan retail nucleation, as represented by sales in the Central Business District and in retail centers, is a consequence of population growth in at least three transportation epochs, the walking and horse era, the electric streetcar era, and the automobile period. Population growth in each epoch has had a different effect on retail nucleation, with the most recent growth having had a pronounced positive effect on development of retail centers and a slight negative effect on the sales of the Central Business District.     

FACTOR STRUCTURE OF THE FAMILY-OF-ORIGIN SCALE: DOES THIS SCALE MEASURE WHAT ITS CREATORS SAY IT DOES?

The factor structure of the Family-of-Origin Scale (FOS) was examined. The FOS is a 40-item instrument devised to measure perceptions of health in the family of origin. Subjects were 162 gay and bisexual males. A confirmatory factor analysis was employed to examine the similarities of the factor structure obtained in the present study with those proposed theoretically by the test authors. The results supported the notion that the FOS is comprised of a single underlying construct that may be represented by bipolar items. It was concluded that the findings do not support the theoretically proposed factor structure of the FOS and that the value of the FOS is suspect.     

Suggestions for Training Students in Using the Internet for Career Counseling

The Internet is increasingly important for career counseling; however, there are few suggestions for training graduate counseling students how to use this technology. This project sought to address that lack by having graduate counseling students use a structured interview with undergraduate volunteer clients to assess which needs could be met using the Internet. Graduate students then identified relevant Web sites and explored these in a meeting with the volunteer clients. Results of class surveys indicated that participants encountered few obstacles using the Internet and perceived this intervention to be useful. Implications for training graduate students in using the Internet for career counseling are discussed.     

The Donation Paradox for Peremptory Challenges

A donation paradox occurs when a player gives an apparently valuable prerogative to another player, but does better, according to some criterion. Peremptory challenges, used in choosing a American jury, permit each side to veto a certain number of potential jurors. With even a very simple model of jury selection, it is shown that for one side to give a peremptory challenge to the other side may lead to a more favorable jury, an instance of the donation paradox. Both a theorem and examples are given concerning the existence of the donation paradox in the optimal use of peremptory challenges.     

Policy Targets and Ethical Tensions: UK Nurse Recruitment

In July 2000 Britain's New Labour government set a target of 20,000 extra nurses for the NHS by 2004. In February 2002, two years ahead of schedule, the target was achieved. The government is to be congratulated on meeting its target but ethical questions over recruitment practices remain. Nurse registrations to the UK from the (then) fifteen EU countries remain flat despite government guidance making this the first priority for international recruitment. Registrations from developing countries with nursing shortages continue despite repeated guidance discouraging this. The government appears to have been caught in a policy bind. On the one hand it needed to be seen to be acting to prevent “poaching” while waiting for fresh intakes of trainees to come through; on the other, if it had succeeded it would have struggled to meet a key policy pledge and certainly not ahead of schedule. New Labour's stated commitment to an ethical foreign policy seems more apparent than real. The paper reports a clear dissonance between the thrust of national policy on nurse recruitment and current employment practices within the UK.     

An Elementary Introduction to Maximum Likelihood Estimation for Multinomial Models: Birch's Theorem and the Delta Method

A fairly complete introduction to the large sample theory of parametric multinomial models, suitable for a second-year graduate course in categorical data analysis, can be based on Birch's theorem (1964) and the delta method (Bishop, Fienberg, and Holland 1975). I present an elementary derivation of a version of Birch's theorem using the implicit function theorem from advanced calculus, which allows the presentation to be relatively self-contained. The use of the delta method in deriving asymptotic distributions is illustrated by Rao's (1973) result on the distribution of standardized residuals, which complements the presentation in Bishop, Fienberg, and Holland. The asymptotic theory is illustrated by two examples.     

Linear Transformations of Linear Mixed-Effects Models

A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.     

Adjusting Cornish–Fisher expansions and confidence intervals for the effect of roundoff

Suppose we want to estimate some smooth function of two types of parameters. The first can be estimated by sample means, while the second is known exactly up to the number of decimal places recorded, that is they are subject to roundoff. We obtain the Cornish–Fisher expansions and associated nonparametric confidence intervals for such functions. These results are illustrated by a simulation study.