THE CONVERGENCE RATE OF SEQUENTIAL FIXED-WIDTH CONFIDENCE INTERVALS FOR REGULAR FUNCTIONALS

Let X₁X₂,.be i.i.d. random variables and let U_n= (n r)^-1S?^(n,r) h (X_i1,., X_ir,) be a U-statistic with EU_n= v, v unknown. Assume that g(X₁) =E[h(X₁,.,X_r) - v |X₁]has a strictly positive variance s?². Further, let a be such that φ(a) - φ(-a) =α for fixed α, 0 < α < 1, where φ is the standard normal d.f., and let S²_n be the Jackknife estimator of n Var U_n. Consider the stopping times N(d)= min {n: S²_n: + n^-1≤²a^-2},d > 0, and a confidence interval for v of length 2d,of the form I_n,d= [U_n,-d, Un + d]. We assume that Var U_n is unknown, and hence, no fixed sample size method is available for finding a confidence interval for v of prescribed width 2d and prescribed coverage probability α Turning to a sequential procedure, let I_N(d),d be a sequence of sequential confidence intervals for v. The asymptotic consistency of this procedure, i.e. lim_{d → 0}P(v ∈ I_N(d),d)=α follows from Sproule (1969). In this paper, the rate at which |P(v ∈ I_N(d),d) converges to α is investigated. We obtain that |P(v ∈ I_N(d),d) - α| = 0 (d^{1/2-(1+k)/2(1+m)}), d → 0, where K = max {0,4 - m}, under the condition that E|h(X₁, X_r)|^m < ∞m > 2. This improves and extends recent results of Ghosh & DasGupta (1980) and Mukhopadhyay (1981).     

Migration differentials by education and occupation: Trends and variations

The effects of education on current migration propensities in the United States are examined for each age group, and an estimate is made of how these age-specific differentials cumulate over a lifetime in determining the number of times that individuals at different educational levels can expect to move over the course of their lives. The independent effects of age, education, and occupation are also examined. Two other sections investigate trends in educational selectivity of migration in the United States and international comparisons of occupational differences in migration.     

Boards of directors: control and decision making in Canadian corporations*

Les statuts légaux spécifient que les corporations doivent être dirigées par un conseil d'administrateurs. Cette étude examine le rôle des directorâts en pouvoir et en contrôle dans un échantillon de corporations manufacturières et découvre, en général, que les conseils n'ont aucune influence sur les prises de décisions. La possession corporative et la composition des conseils sont reconnus comme d'importants facteurs qui affectent les structures de contrôles. Si la possession est concentree sur une base origine-filiale, le contrôle tend àêtre levé par l'enchaînement de gérance. Quand la possession est largement concentrée chez les directeurs, ceux-ci sont en lieu de retenir le contrôle. Si la possession est établie par des actionnaires qui ne sont pas les directeurs, la directive aura des degrés variants de contrôle dans les prises de décisions, dépendant sur la concentration de cette possession. Si la directive contient des courtiers, il est plus possible d'y avoir une fonction de contrôle dans les prises de décisions que quand la corporation est composée entièrement d'initiés. Legal statutes specify that corporations shall be managed by a board of directors. This study examines the role of directorates in power and control in a sample of manufacturing corporations and finds, in general, that most boards are not influential in decision making. Corporate ownership and board composition are found to be important factors affecting control patterns. If ownership is concentrated on a parent-subsidiary basis, control tends to be exercised through management links. When ownership is largely by managers, they are likely to retain control. If ownership is by nonmanager shareholders, then the board will have varying degrees of control in decision making, depending on the concentration of that ownership. If the board contains outsiders, then it is more likely to have a control function in corporate decision making than when it is composed solely of insiders.     

New places — New identities: Settings in the lives of the old

This paper addresses the relationship between meaning attached to settings by social actors and their self-identities. In the context of research on the social worlds of old widows the author identifies “ideal type” self-designated identities, namely that of “resident” vs. “newcomer” in a setting. These self-identities are considered in light of the bearing upon them of the non-human or physical aspects of settings as well as of the people who share the settings. Finally, strategies for maintaining “resident” status are shown to be more limited for the old than for the younger members of society. I would like to thank Juanita B. Wood, Stephen G. Wieting, Ellen Horgan Biddle, Harold B. Freshley, and an anonymous reviewer forQualitative Sociology for their instructive comments on earlier drafts of this paper. This research was supported in part by a grant from the Administration on Aging, Department of Health, Education, and Welfare. Researchers undertaking such projects are encouraged to express freely their professional judgment. Therefore, points of view or opinions stated in this document do not necessarily represent the official position or policy of the Department of Health, Education, and Welfare.     

AN EVOLUTIONARY MODEL OF TASTE FOR RISK

Economists take tastes as given. However, tastes must be derived from biological models of evolutionary survival; we exhibit those tastes which served to make our ancestors survive. In particular, economists have no theory which explains observed behavior towards risk; rather, we take behavior as a datum. In this paper we present a model which explains risk seeking by adolescents and risk aversion by mature males as the result of an evolutionary mechanism.