Accurate Confidence Interval Estimation of Small Area Parameters Under the Fay–Herriot Model

Small area estimation has long been a popular and important research topic due to its growing demand in public and private sectors. We consider here the basic area level model, popularly known as the Fay–Herriot model. Although much of current research is predominantly focused on second order unbiased estimation of mean squared prediction errors, we concentrate on developing confidence intervals (CIs) for the small area means that are second order correct. The corrected CI can be readily implemented, because it only requires quantities that are already estimated as part of the mean squared error estimation. We extend the approach to a CI for the difference of two small area means. The findings are illustrated with a simulation study.     

Predictors of children's understandings of death: age, cognitive ability, death experience and maternal communicative competence

A child's age, cognitive ability, and exposure to death in the environment have been documented as major factors affecting the formation of a mature death concept. The present study investigated the relationships between these three factors (age, cognitive ability, and death experience) and children's understandings of death, as well as the relationship between mothers' communicative competence and children's understandings of death. Thirty-seven children (ages 48-96 months) completed three cognitive tasks and answered four dichotomous questions about death. Their mothers (N = 37) responded in writing to 16 questions about death that children are likely to ask. Results showed significant relationships between age and understanding, between seriation ability and understanding, and between death experience and understanding. There was no statistically significant relationship between maternal response competence and children's understandings of death. Implications are discussed.     

A note on homogeneity tests of covariance matrices

In this note we propose two procedures for testing homogeneity of co-variance matrices that are both extensions of Hartley's (1940) test for equality of variances. The first is a two-stage procedure where the first step is a simple test for equality of the largest eigenvalues, and corresponding eigenvectors, of the covariance matrices. The second is based on projection pursuit and seems harder to apply in practice.     

A continuous repeated measurements model:the experimental design problem with fixed time constraints

A repeated measurements model where the within-subject response is modeled as a continuous time regression is analyzed using reproducing kernel Hilbert space methods, Parzen (1961). The basic goal is to study the statistical design problem when experimental units and measurements are "free", but the total measurement time is fixed. This kind of situation arises when the experiment uses scarce resources such as space or oceanographic platforms or a magnetic resonance imaging (MRI) device. In this situation the only constraint is the total time allocated to the experiment.     

The Performance of Periodic Autoregressive Models in Forecasting Seasonal U.K. Consumption

The parameters of a periodic model are allowed to vary according to the time at which observations are made. Periodic autoregressive models are fitted to the quarterly values of seasonally unadjusted real nondurable consumers' expenditure for the United Kingdom and its components. The periodic model offers no improvement over conventional specifications if the aggregate is modeled directly. On the other hand, periodic models generally perform well for the components, which contain additional seasonal information. The choice between a periodic or nonperiodic specification is also shown to have an important influence on the resulting dynamic properties.     

Extensions of multiple linear regression

Many statistical methods are linked together through their connection with weighted least squares and hence regression. This article reviews these connections, emphasising the iteratively weighted least squares algorithm.     

Some results on interval estimation for the two-parameter weibull or extreme-value distribution

Two statistics based on simple, closed form estimators are examined for use in interval estimation of reliability and of the location parameter of the extreme-value distribution. Properties of the estimators are studied by Monte Carlo simulation, and procedures for interval estimation and tests of hypotheses for the location parameter and reliability are provided.