Five legitimate definitions of correlated equilibrium in games with incomplete information

Aumann's (1987) theorem shows that correlated equilibrium is an expression of Bayesian rationality. We extend this result to games with incomplete information.First, we rely on Harsanyi's (1967) model and represent the underlying multiperson decision problem as a fixed game with imperfect information. We survey four definitions of correlated equilibrium which have appeared in the literature. We show that these definitions are not equivalent to each other. We prove that one of them fits Aumann's framework; the agents normal form correlated equilibrium is an expression of Bayesian rationality in games with incomplete information.We also follow a universal Bayesian approach based on Mertens and Zamir's (1985) construction of the universal beliefs space. Hierarchies of beliefs over independent variables (states of nature) and dependent variables (actions) are then constructed simultaneously. We establish that the universal set of Bayesian solutions satisfies another extension of Aumann's theorem.We get the following corollary: once the types of the players are not fixed by the model, the various definitions of correlated equilibrium previously considered are equivalent.     

Conspicuous conservatism in risk choice

We analyze the risk levels chosen by agents who have private information regarding their quality, and whose performance will be judged and rewarded by outsiders. Assume that risk choice is observable. Agents will choose risk strategically to enhance their expected reputations. We show that conspicuous conservatism results: agents of different qualities choose levels below those that would be chosen if quality were observable. This happens because bad agents must cloak their identity by choosing the same risk level as good agents, and good agents are more likely to distinguish themselves if they reduce the risk level. Our results contrast starkly with those for the case when risk choice cannot be observed.

Variance estimation when donor imputation is used to fill in missing values

Donor imputation is frequently used in surveys. However, very few variance estimation methods that take into account donor imputation have been developed in the literature. This is particularly true for surveys with high sampling fractions using nearest donor imputation, often called nearest‐neighbour imputation. In this paper, the authors develop a variance estimator for donor imputation based on the assumption that the imputed estimator of a domain total is approximately unbiased under an imputation model; that is, a model for the variable requiring imputation. Their variance estimator is valid, irrespective of the magnitude of the sampling fractions and the complexity of the donor imputation method, provided that the imputation model mean and variance are accurately estimated. They evaluate its performance in a simulation study and show that nonparametric estimation of the model mean and variance via smoothing splines brings robustness with respect to imputation model misspecifications. They also apply their variance estimator to real survey data when nearest‐neighbour imputation has been used to fill in the missing values. The Canadian Journal of Statistics 37: 400–416; 2009 © 2009 Statistical Society of Canada     

On the almost unbiased generalized liu estimator and unbiased estimation of the bias and mse

In this paper, we derive the almost unbiased generalized Liu estimator and examine an exact unbiased estimator of the bias and mean squared error of the feasible generalized Liu estimator . We compare the almost unbiased generalized Liu estimator (AUGLE) with the generalized Liu estimator (GLE) and with the ordinary least squares estimator (OLSE).     

Child custody issues and co‐occurrence of intimate partner violence and child maltreatment: controversies and points of agreement amongst practitioners

The situation of families undergoing separation in a context of co‐occurrence of intimate partner violence (IPV) and child maltreatment raises certain issues related to child custody. The results presented in this paper were collected and analysed within the framework of a qualitative study aiming to identify the principal points of agreement and the main controversies amongst practitioners in several different types of organizations. Focus groups were held with a total of 43 practitioners from six different settings concerned with child custody in cases of co‐occurrence of IPV and child maltreatment. Although they agreed on the importance of ensuring the safety of victims of violence, their views diverged on three points: (1) the importance of preserving the father–child relationship; (2) collaboration between voluntary organizations and semi‐voluntary or legal agencies; and (3) consideration of cultural differences.     

The Effects of Perceived Barriers,Role Models,and Acculturation on the Career Self‐Efficacy and Career Consideration of Hispanic Women

This study used path analysis to examine the relationship between perceived barriers, acculturation, and role model influence on the career self‐efficacy and career considerations of a sample of Hispanic women. Two path models were examined. The male‐dominated model accounted for 15% of the variance, and the female‐dominated model accounted for 26% of the variance. No relationship was found between the variables of interest and male‐dominated career self‐efficacy and consideration. However, perceived barriers were related to female‐dominated career consideration and Anglo acculturation significantly contributed to female‐dominated career self‐efficacy. Results are discussed with regard to career practice and research with Hispanic women.     

Children In Poverty: The Fundamental Issue

According to the Census Bureau, 21.9 percent of children in the United States in 1992 were poor (25 percent if one considers only those under six). Those 14.6 million children comprise 40 percent of the total population living below the poverty line. This essay documents their plight, examines the secondary effects of poverty upon the person and community, analyzes why the current “subsidy” approach has been ineffective, seeks a holistic explanation for poverty, and proposes a universal approach based on “supplementation” and “empowerment.” Due to the present budget deficit, the program is designed to be revenue neutral; it should not require any additional taxes.     

A multistate approach for estimating the incidence of human immunodeficiency virus by using data from a prevalent cohort study

Summary.  Cohort studies of individuals infected with the human immunodeficiency virus (HIV) provide useful information on the past pattern of HIV diagnoses, progression of the disease and use of antiretroviral therapy. We propose a new method for using individual data from an open prevalent cohort study to estimate the incidence of HIV, by jointly modelling the HIV diagnosis, the inclusion in the cohort and the progression of the disease in a Markov model framework. The estimation procedure involves the construction of a likelihood function which takes into account the probability of observing the total number of subjects who are enrolled in the cohort and the probabilities of passage through the stages of disease for each observed subject conditionally on being included in the cohort. The estimator of the HIV infection rate is defined as the function which maximizes a penalized likelihood, and the solution of this maximization problem is approximated on a basis of cubic M -splines. The method is illustrated by using cohort data from a hospital-based surveillance system of HIV infection in Aquitaine, a region of south-western France. A simulation study is performed to study the ability of the model to reconstruct the incidence of HIV from prevalent cohort data.     

The family and adults 65 years of age and over

The policy makers usually assume that the nuclear family model is almost universally favoured in our industrial and urban society. Governmental agencies are thus left with the responsibility taken over in the past by the extended family. Gerontological literature studied the family support available to the elderly. In general, research results have supported the modified extended family model. Here, the multigenerational household is defined as a living arrangement in contradiction with the nuclear family model, but able to provide support to the disabled elderly. With three random samples of non-institutionalized francophone elderly, it was possible to estimate the number of elderly people living in multigenerational households. It was observed that the elderly in such households are older and more functionally impaired than the elderly living in other kinds of households. Thus, the multigenerational household offers a potential for support neglected by policy makers. Governmental agencies should see themselves as supporters of family involvement with elderly members rather than as surrogates for the family. Les planificateurs assument que la famille nucléaire est le modèle presqu'unique adopte par les families de sociétés industrielles et urbaines. Les agences gouvernementales doivent done prendre la reléve de la famille ètendue. Les recherches en gérontologie ont pourtant démontrv que l'aide familiale est disponible aux personnes âgées. En fait, la famille contemporaine assure la plus grande part de l'aide aux personnes âgées. Le ménage multi-générationel se pose en source importante de support pour la personne âgée qui en est membre. L'observation de trois échantillons aléatoires de personnes âgées urbaines et francophones permet une estimation du nombre de personnes âgées habitant dans un ménage multigénérationel. En plus, ces personnes sont plus âgées et ont plus d'incapacités fonctionnelles que les personnes âgées seules ou vivant avec leur conjoint seulement. En conséquence, la famille nucléaire n'est pas un modèle empiriquement adéquat. Les recherches ont plutôt proposé le modèle de la famille étendue modifiée. Les agences gouvernementales devraient concevoir leur rôle en fonction du support qu'offre la famille â ses membres âgés plutôt que de se définir comme substituts familiaux.