Breakdown points for redescending m-estimates of location

Breakdown point is one measure of the robustness of an estimate. This paper discusses some unusual properties of the breakdown points of M-estimates of location.     

Further results on the two-stage hierarchial information (2shi) estimators in the linear regression models

The paper considers a class of 2SHI estimators for the linear regression models and provides some results regarding the dominance in quadratic loss of this class over the OLS and usual Stein-rule estimators.     

Modelling forces of infection by using monotone local polynomials

Summary. On the basis of serological data from prevalence studies of rubella, mumps and hepatitis A, the paper describes a flexible local maximum likelihood method for the estimation of the rate at which susceptible individuals acquire infection at different ages. In contrast with parametric models that have been used before in the literature, the local polynomial likelihood method allows this age-dependent force of infection to be modelled without making any assumptions about the parametric structure. Moreover, this method allows for simultaneous nonparametric estimation of age-specific incidence and prevalence. Unconstrained models may lead to negative estimates for the force of infection at certain ages. To overcome this problem and to guarantee maximal flexibility, the local smoother can be constrained to be monotone. It turns out that different parametric and nonparametric estimates of the force of infection can exhibit considerably different qualitative features like location and the number of maxima, emphasizing the importance of a well-chosen flexible statistical model.     

Minimax estimation of a lower-bounded scale parameter of a gamma distribution for scale-invariant squared-error loss

Let X have a gamma distribution with known shape parameter θr;aL and unknown scale parameter θ. Suppose it is known that θ ≥ a for some known a > 0. An admissible minimax estimator for scale-invariant squared-error loss is presented. This estimator is the pointwise limit of a sequence of Bayes estimators. Further, the class of truncated linear estimators C = {θ_ρ|θ_ρ(x) = max(a, ρ), ρ > 0} is studied. It is shown that each θ_ρ is inadmissible and that exactly one of them is minimax. Finally, it is shown that Katz's [Ann. Math. Statist., 32, 136–142 (1961)] estimator of θ is not minimax for our loss function. Some further properties of and comparisons among these estimators are also presented.     

An empirical Bayes approach to outliers

A formulation of the problem of detecting outliers as an empirical Bayes problem is studied. In so doing we encounter a non-standard empirical Bayes problem for which the notion of average risk asymptotic optimality (a.r.a.o.) of procedures is defined. Some general theorems giving sufficient conditions for a.r.a.o. procedures are developed. These general results are then used in various formulations of the outlier problem for underlying normal distributions to give a.r.a.o. empirical Bayes procedures. Rates of convergence results are also given using the methods of Johns and Van Ryzin (1971, 1972).     

The Imaginary Audience and Personal Fable: Factor Analyses and Concurrent Validity of the “New Look” Measures

This study examined key components of the “New Look” at the imaginary audience and personal fable constructs. Toward this end, data from four samples of Belgian high school students (N= 1,458) were analyzed. Confirmatory and exploratory factor analyses failed to confirm that the measures associated with the New Look theory, the New Imaginary Audience Scale, and the New Personal Fable Scale (NPFS), tapped a common underlying construct. Only the invulnerability and omnipotence subscales of the NPFS proved to be highly related. In line with the New Look theory, boys were found to believe more strongly in their own uniqueness, invulnerability, and omnipotence than were girls. Higher scores on the invulnerability and omnipotence subscales were associated with lower levels of depression and loneliness. Finally, each aspect of the personal fable seemed to have its own specific role in the process of separation – individuation. Implications of these findings for the New Look theory of the imaginary audience and the personal fable are discussed. Suggestions for future research are put forth, with particular emphasis on the role of the invulnerability/omnipotence complex in adolescent development and behavior and on the family resemblances among the various aspects of the personal fable.