Statistical consulting

The paper and the special issue focus on the activity of statistical consulting and its varieties. This includes academic consulting, consulting to and in industry as well as statistics in public media.     

Shrinkage confidence intervals for the normal mean: Using a guess for greater efficiency

If the unknown mean of a univariate population is sufficiently close to the value of an initial guess then an appropriate shrinkage estimator has smaller average squared error than the sample mean. This principle has been known for some time, but it does not appear to have found extension to problems of interval estimation. The author presents valid two‐sided 95% and 99% “shrinkage” confidence intervals for the mean of a normal distribution. These intervals are narrower than the usual interval based on the Student distribution when the population mean lies in such an “effective interval.” A reduction of 20% in the mean width of the interval is possible when the population mean is sufficiently close to the value of the guess. The author also describes a modification to existing shrinkage point estimators of the general univariate mean that enables the effective interval to be enlarged.     

A Sparse Implementation of the Average Information Algorithm for Factor Analytic and Reduced Rank Variance Models

Factor analytic variance models have been widely considered for the analysis of multivariate data particularly in the psychometrics area. Recently Smith, Cullis & Thompson (2001) have considered their use in the analysis of multi‐environment data arising from plant improvement programs. For these data, the size of the problem and the complexity of the variance models chosen to account for spatial heterogeneity within trials implies that standard algorithms for fitting factor analytic models can be computationally expensive. This paper presents a sparse implementation of the average information algorithm (Gilmour, Thompson & Cullis, 1995) for fitting factor analytic and reduced rank variance models.     

Some results on optimality in models with heteroscedastic errors from partial optimum designs

This paper studies optimum designs for linear models when the errors are heteroscedastic. Sufficient conditions are given in order to obtainD-, A- andE-optimum designs for a complete regression model from partial optimum designs for some sub-parameters. A result about optimality for a complete model from the optimality for the submodels is included. Supported by Junta de Andalucía, research group FQM244.     

A “brer rabbit” case for reverse mandated benefits

Reverse mandated benefits is a government-mandated policy that requires employees to provide their employers with benefits that workers would not provide otherwise. Of course, only those benefits would be mandated that are worth more to employers than they cost, as determined by political authorities. My case for such a policy argues that it is at least as sensible as policies mandating that employers provide benefits to their employees that would not be provided otherwise.     

Intertemporal choice under timing risk: An experimental approach

This paper investigates how individuals evaluate delayed outcomes with risky realization times. Under the discounted expected utility (DEU) model, such evaluations depend only on intertemporal preferences. We obtain several testable hypotheses using the DEU model as a benchmark and test these hypotheses in three experiments. In general, our results show that the DEU model is a poor predictor of intertemporal choice behavior under timing risk. We found that individuals are averse to timing risk and that they evaluate timing lotteries in a rank-dependent fashion. The main driver of timing risk aversion is nothing but probabilistic risk aversion that stems from the nonlinear treatment of probabilities.     

Violations of dominance in pricing judgments

The dominance principle states that the judged price of gamble A should be equal to or greater than the judged price of gamble B whenever A's outcomes are equal to or better than the corresponding outcomes of B, holding everything else constant. Subjects often violate the dominance principle by assigning a higher price to a gamble with some probability of winning a positive amount, Y, otherwise zero, than to a superior gamble with the same chances of winning Y, otherwise winning X. Violations also occur with losses. Results are consistent with a configural-weight theory in which the decision weight for each outcome depends on the rank of the outcome with respect to the other outcomes in the lottery and the value of the outcome (zero vs. nonzero).The authors thank Shi-jie Chang, Duncan Luce, and Lisa Ordóñez for comments on an earlier draft. This research was supported by a National Science Foundation grant to the first author (BNS-8451368). Requests for reprints should be sent to Barbara Mellers, Dept. of Psychology, University of California, Berkeley, CA 94720.