Estimation from current-status data in continuous time

The nonparametric maximum likelihood estimator for current-status data has been known for at least 40 years, but only recently have the mathematical-statistical properties been clarified. This note provides a case study in the important and often studied context of estimating age-specific immunization intensities from a seroprevalence survey. Fully parametric and spline-based alternatives (also based on continuous-time models) are given. The basic reproduction number R ₀ exemplifies estimation of a functional. The limitations implied by the necessarily rather restrictive epidemiological assumptions are briefly discussed.     

Heights of representative systems: A proof of Fishburn's conjecture

Representative systems with n-voters are hierarchical choice functions from {-1, 0, 1} ⁿ to {-1, 0, 1} constructed as iterations of weighted majority voting. The height of a representative system is the minimal number of iterations necessary for this construction.In the paper we give an upper bound for (n), the maximal height of any n-voter representative system, and show that goes to zero as n goes to infinity, thus proving a conjecture made by Fishburn. Technically, the results are obtained by transferring the problem to the context of proper simple games, which have a similar hierarchical structure, and using known results on heights of simple games.     

Modelling excess mortality of the unemployed: choice of scale and extra-Poisson variability

"Occupational mortality and morbidity is usually studied via standardized mortality (or morbidity) ratios, with little attention to the basic fit of the implicit underlying proportional hazards model. This paper presents a case study on unemployment and mortality, based on the complete Danish male population aged 20-64 years at the 1970 census. The effect of unemployment on the age-specific mortality rate is intermediate between additive and multiplicative and was fitted well by an additive effect on the square root of the mortality. The paper discusses and illustrates whether finer stratification or random residual variation ('frailty') is to be preferred for obtaining a statistically satisfactory fit."     

Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization

The concept of coalition proof Nash equilibrium was introduced by Bernheim et al. [5]. In the present paper, we consider the representation problem for coalition proof Nash equilibrium: For a given effectivity function, describing the power structure or the system of rights of coalitions in society, it is investigated whether there is a game form which gives rise to this effectivity function and which is such that for any preference assignment, there is a coalition proof Nash equilibrium.  It is shown that the effectivity functions which can be represented in coalition proof Nash equilibrium are exactly those which satisfy the well-known properties of maximality and superadditivity. As a corollary of the result, we obtain necessary conditions for implementation of a social choice correspondence in coalition proof Nash equilibrium which can be formulated in terms of the associated effectivity function. Received: 24 June 1999/Accepted: 20 September 2000     

Empirical Bayes Age–Period–Cohort Analysis of Retrospective Incidence Data

We analyse the (age, time)-specific incidence of diabetes based on retrospective data obtained from a prevalent cohort only including survivors to a particular date. From underlying point processes with intensities corresponding to the (age, time)-specific incidence rates the observed point pattern is assumed to be generated by an independent thinning process with parameters (assumed known) depending on population density and survival probability to the sampling date. A Bayesian procedure is carried out for the optimal adjustment and comparison of isotropic and anisotropic smoothing priors for the intensity functions, as well as for the decomposition of the intensity on the (time, age) Lexis diagram into the three factors of age, period and cohort.     

Explained Variation and Predictive Accuracy in General Parametric Statistical Models: The Role of Model Misspecification

When studying a regression model measures of explained variation are used to assess the degree to which the covariates determine the outcome of interest. Measures of predictive accuracy are used to assess the accuracy of the predictions based on the covariates and the regression model. We give a detailed and general introduction to the two measures and the estimation procedures. The framework we set up allows for a study of the effect of misspecification on the quantities estimated. We also introduce a generalization to survival analysis.     

Minimal manipulability and interjacency for two-person social choice functions

This paper investigates the number of profiles at which a social choice function is manipulable. It is found that there is a lower bound on this number when the social choice function is assumed non-dictatorial. Also, any number between this lower bound and the maximal number of profiles may be obtained as the number of manipulable profiles of some social choice function. Received: 30 November 1993 / Accepted: 14 April 1997