On the relative efficiency of a monotone parameter curve estimator in a functional nonlinear model

Functional regression models that relate functional covariates to a scalar response are becoming more common due to the availability of functional data and computational advances. We introduce a functional nonlinear model with a scalar response where the true parameter curve is monotone. Using the Newton-Raphson method within a backfitting procedure, we discuss a penalized least squares criterion for fitting the functional nonlinear model with the smoothing parameter selected using generalized cross validation. Connections between a nonlinear mixed effects model and our functional nonlinear model are discussed, thereby providing an additional model fitting procedure using restricted maximum likelihood for smoothing parameter selection. Simulated relative efficiency gains provided by a monotone parameter curve estimator relative to an unconstrained parameter curve estimator are presented. In addition, we provide an application of our model with data from ozonesonde measurements of stratospheric ozone in which the measurements are biased as a function of altitude.     

Some notes on the fisher–bingham family on the sphere

The fisher–Bingham family is potentially useful class of spherical distributions, but its practical application has been hindered by various problems, including; the identification of the form of the distribution, given the parameter values; and finding an effective technique for calculating the normalising constant, a requirement for maximum likelihood estimation. It is explained how these difficulties can be resolved. and then parameter estimation and hypothesis testing are discussed. A practical example is given.     

Generalized EM estimation for semi-parametric mixture distributions with discretized non-parametric component

We consider independent sampling from a two-component mixture distribution, where one component (called the parametric component) is from a known distributional family and the other component (called the non-parametric component) is unknown. This is a semi-parametric mixture distribution. We discretize the non-parametric component and estimate the parameters of this mixture model, namely the mixing proportion, the unknown parameters of the parametric component and the discretized non-parametric component. We define the maximum penalized likelihood (MPL) estimates of the mixture model parameters and then develop a generalized EM (GEM) iterative scheme to compute the MPL estimates. A simulation study and an example from biology are presented.     

Social-cognitive Competence, Peer Rejection and Neglect, and Behavioral and Emotional Problems in Middle Childhood

This prospective, longitudinal study examines individual differences in two conceptually related but empirically distinct domains of social-cognitive competence (cognitive interpretive understanding and interpersonal perspective co-ordination) as moderators of the relation between peer rejection and neglect and behavioral and emotional problems in grades 2 and 3. As expected, peer rejection and neglect increased risks for behavioral and emotional problems whereas interpretive understanding (understanding of mental states) and perspective co-ordination (awareness of others' emotions and motives) reduced risks for aggressive, disruptive, inattentive, and anxious, sad, withdrawn behaviors. Assumptions that awareness of others' perspectives bestows consistent benefits for children experiencing peer problems were challenged. Unexpectedly, rejection and neglect increased risks for behavioral and emotional problems for children who demonstrated average and high levels of perspective co-ordination. More advanced perspective co-ordination may heighten children's sensitivity to peer relationship problems and result in general maladjustment, both concurrently and over time. Less advanced perspective co-ordination may also be responsible for the 'optimistic bias' that has been noted in aggressive children.     

Refusal Bias in the Estimation of HIV Prevalence

In 2007, UNAIDS corrected estimates of global HIV prevalence downward from 40 million to 33 million based on a methodological shift from sentinel surveillance to population-based surveys. Since then, population-based surveys are considered the gold standard for estimating HIV prevalence. However, prevalence rates based on representative surveys may be biased because of nonresponse. This article investigates one potential source of nonresponse bias: refusal to participate in the HIV test. We use the identity of randomly assigned interviewers to identify the participation effect and estimate HIV prevalence rates corrected for unobservable characteristics with a Heckman selection model. The analysis is based on a survey of 1,992 individuals in urban Namibia, which included an HIV test. We find that the bias resulting from refusal is not significant for the overall sample. However, a detailed analysis using kernel density estimates shows that the bias is substantial for the younger and the poorer population. Nonparticipants in these subsamples are estimated to be three times more likely to be HIV-positive than participants. The difference is particularly pronounced for women. Prevalence rates that ignore this selection effect may be seriously biased for specific target groups, leading to misallocation of resources for prevention and treatment.     

Variance Reduction Using Nonlinear Controls and Transformations

Nonlinear regression-adjusted control variables are investigated for improving variance reduction in statistical and system simulations. To this end, simple control variables are piecewise sectioned and then transformed using linear and nonlinear transformations. Optimal parameters of these transformations are selected using linear or nonlinear least-squares regression algorithms. As an example, piecewise power-transformed variables are used in the estimation of the mean for the twovariable Anderson-Darling goodness-of-fit statistic W ₂ ². Substantial variance reduction over straightforward controls is obtained. These parametric transformations are compared against optimal, additive nonparametric transformations obtained by using the ACE algorithm and are shown, in comparison to the results from ACE, to be nearly optimal.     

The earnings of men and remarriage

Focusing on the effects of men's earnings, this paper analyzes remarriage. Previous empirical research has not established what theoretical aspects of men's earnings are important. Here, data for Wisconsin high school graduates that include male respondents' Social Security earnings history are analyzed. The results indicate that absolute earnings, earnings instability, and earnings relative to peers have minimal effects on a man's probability of remarriage, but that permanent income positively affects remarriage. However, studies of marital disruption often find permanent income is not as important as relative earnings measures. Concluding remarks speculate about the meaning of these contrasting findings for the economics of marriage.