M-Estimates of regression when the scale is unknown and the error distribution is possibly asymmetric: A minimax result

Huber (1964) found the minimax-variance M-estimate of location under the assumption that the scale parameter is known; Li and Zamar (1991) extended this result to the case when the scale is unknown. We consider the robust estimation of the regression coefficients (β₁,…,β_p) when the scale and the intercept parameters are unknown. The minimax-variance estimates of (β₁,…,β_p) with respect to the trace of their asymptotic covariance matrix are derived. The maximum is taken over ?-contamination neighbourhoods of a central regression model with Gaussian errors (asymmetric contamination is allowed), and the minimum is taken over a large class of generalized M-estimates of regression of the Mallow type. The optimal choice of estimates for the nuisance parameters (scale and intercept) is also considered.     

Labor force participation and family formation: A study of working mothers

Drawing upon a sample of 638 mothers aged 18 to 40, with at least some marital work experience, significant associations were found between the extent, kind, and timing of employment and a series of family formation variables. Generally lower fertility, longer first birth intervals, and earlier use of birth control were associated with the longest work durations, the highest status jobs, and work before the birth of the first child. The data failed, however, to differentiate desired family size.     

Arbitrators’ backgrounds and behavior

Evidence indicates that when choosing arbitrators biographical information about them is used by labor and management representatives. Presumably, this helps ensure selection of the “right” arbitrator, behaviorally speaking. The present study assessed the general utility of this practice by examining the relationship between biographical information and arbitrator behavior for 250 arbitrators. It was found that the biographical information accounted for only small portions of the variance in four measures of arbitrator behavior. Implications are discussed in terms of arbitrator selection practices and future research needs. This research was conducted while the first author was on leave at Ohio State University from the University of Wisconsin-Madison. The authors wish to thank Cathy Collins, Reba Leiding, Rufus Milsted, and Grace Winslow for their assistance on this project. A version of this paper was presented at the annual meeting of the Industrial Relations Research Association, New York, December 1982.     

The reversal small-world experiment

This paper is an attempt to examine and define the world network of a typical individual by discovering how many of his or her acquaintances could be used as first steps in a small-world procedure, and for what reasons. The town and occupation of each target was provided, together with the ethnic background, where this could not be inferred from the name. Starters were instructed in the small-world experiment and asked to write down their choice, amongst the people they knew, for the first link in a potential chain from them to each of 1267 targets. Starters provided information on each choice made (e.g. mother, cousin, friend, acquaintance, etc.) together with the sex of the choice) and the reason that choice had been made. The reason could be in one or more of four categories: something about the location of the target caused the starter to think of his or her choice; the occupation of the target was responsible for the choice; the ethnicity of the target; or some other, unspecified, reason.Six main conclusions may be drawn from the data: (1) A mean of 210 choices per starter account for the “world” (i.e. the 1267 targets). This number is probably an underestimate. Only 35 choices are necessary to account for half the world, however. Of the 210, 95 (45%) were chosen most often for location reasons, 99 (47%) were chosen most often for occupation reasons, and only 7% of the choices were mainly based on ethnicity or other reasons. (2) Choices were mainly friends and acquaintances, with strong cleavage by sex. For any given target, the type of choice used by the majority of starters was a friend or acquaintance, and not family. For any given target, the most likely sex of the choice (i.e. over all starters) can be predicted accurately on 82% of occasions. This sex tends to be male, unless both starter and target are female, or if the target has a low-status occupation. Additionally, any given starter is most likely to pick a male choice for any target, except for the female starter-female target combination, when female choices are more likely. This was correct on 64% of occasions. (3) Location was the usual reason for choice (out of the four categories), with occupation second, and ethnicity or other reasons rarely used. This most popular reason for choice may be correctly predicted for any given target 81% of the time. (4) The decision as to which choice was made appears to depend primarily on the occupation of the target, and secondly on the distance (near/far) from Morgantown, West Virginia, where the experiment took place. (5) The expression “having one's man in …” can be partially quantified. We may define a choice to “handle” a state in the U.S. if he or she was chosen for two-thirds or more of the targets in that state for which choices were made on the basis of location. Then, for any starter, on average, half the states are each handled by a single choice. (6) The accuracy of starters' recall about their networks is low, in the sense that their recall is incorrect more often than it is correct (i.e. their recall could not be put to any other use with any reliability). This confirms previous experiments on informant accuracy.     

Plague mortality rates by age and sex in the parish of St. Botolph's without Bishopsgate, London, 1603

Abstract The Bills of Mortality for London were instituted at least as early as 1528 but only a few figures survive before the extant annual series that begins in 1603. Ages at death, even in broad groups of ages, are not generally available until 1728, which is more than 50 years too late to give us any inkling of the ages, if any, at which people were specially susceptible to plague. There are reports, it is true, that suggest that children suffered from plague more severely than adults, at least on certain occasions (as in 1361 or 1418 for example), but nothing more precise. The legend of the Pied Piper of Hamelin may be a folk-memory of a plague (possibly in 1284) that killed mainly the children of the town, for the connection between infestation of rats and the loss of children suggests some kind of plague outbreak. Pollitzer concludes that no particular age group is specially liable to plague, and attributes all differences observed to different risks of exposure. The determinants of the severity of an outbreak would therefore be the environmental details and social customs.     

A Bayesian view of assessing uncertainty and comparing expert opinion

A Bayesian approach to the problem of comparing experts or expert systems is presented. The question of who is an expert is considered and comparisons among well-calibrated experts are studied. The concept of refinement, in various equivalent forms, is used in this study. An informative example of the combination of the opinions of well-calibrated experts is described. Total orderings of the class of well-calibrated experts are derived from strictly proper scoring rules.