Bibliographical Note

In England in the Middle Ages, inheritance data were recorded of tenants who owned land from the Crown. Male adult mortality is estimated from these data. A tenant was allowed to sell his land. Only if he still owned land at death, his age at death was observed; so death was right censored by sell of all the land. The censoring times are not observed because sell of land was never recorded. This makes the estimation problem nonstandard. The age at death is left truncated, because a future tenant had to survive his testator to inherit the title “tenant” and the land and to appear in the dataset. Life span distribution and life expectancy are estimated before and during the outbreak of the Black Death, which started in 1348.     

The Relations Among Relatedness Needs,Subjective Well-Being,and Depression of Korean Elderly

The first part of the study examined what the relatedness needs Korean elderly have in close relationships (spouse, children, friends) are. The most salient needs were “love and care” for spouse and “contact and often meeting” for children and friends. The second part of the study assessed the relations among the difference between expectation and satisfaction of relatedness needs, subjective well-being, and depression of Korean elderly. Regression analyses showed that the difference between expectation and satisfaction of relatedness needs for spouse and children significantly predicted subjective well-being and depression. Finally, gender differences are discussed in terms of the patriarchal culture of Korean society.     

Didn't we just see you? Time to recurrence among frequently encountered families in CPS

In child protection services, multiple maltreatment recurrences, or chronic maltreatment, has been a concern drawing increased attention because of its persistent harm to the children and the need to consider more effective intervention strategies to meet its unique needs. Timing has been an important issue in understanding the pattern of chronic maltreatment. No existing research has examined the influence of the interval between previous maltreatment incidents on future recurrences. The current study uses state administrative data to conduct longitudinal analyses to examine how the interval between previous maltreatment incidents is associated with the likelihood of future maltreatment occurrence among children who encountered multiple maltreatment recurrences. The findings suggest that short intervals are associated with increased likelihood of encountering a future recurrence, while controlling various covariates. The findings suggest the possibility of including the interval between previous maltreatment incidents as an indicator for child maltreatment risk assessment, and the need for developing responsive intervention strategies to stop the trend of chronic maltreatment.     

Maximum likelihood vs. maximum goodness of fit estimation of the three-parameter Weibull distribution

The use of statistics based on the empirical distribution function is analysed for estimation of the scale, shape, and location parameters of the three-parameter Weibull distribution. The resulting maximum goodness of fit (MGF) estimators are compared with their maximum likelihood counterparts. In addition to the Kolmogorov–Smirnov, Cramer–von Mises, and Anderson–Darling statistics, some related empirical distribution function statistics using different weight functions are considered. The results show that the MGF estimators of the scale and shape parameters are usually more efficient than the maximum likelihood estimators when the shape parameter is smaller than 2, particularly if the sample size is large.     

Bayes estimation and prediction of the two-parameter gamma distribution

In this article, the Bayes estimates of two-parameter gamma distribution are considered. It is well known that the Bayes estimators of the two-parameter gamma distribution do not have compact form. In this paper, it is assumed that the scale parameter has a gamma prior and the shape parameter has any log-concave prior, and they are independently distributed. Under the above priors, we use Gibbs sampling technique to generate samples from the posterior density function. Based on the generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct HPD credible intervals. We also compute the approximate Bayes estimates using Lindley's approximation under the assumption of gamma priors of the shape parameter. Monte Carlo simulations are performed to compare the performances of the Bayes estimators with the classical estimators. One data analysis is performed for illustrative purposes. We further discuss the Bayesian prediction of future observation based on the observed sample and it is seen that the Gibbs sampling technique can be used quite effectively for estimating the posterior predictive density and also for constructing predictive intervals of the order statistics from the future sample.     

Model selection and parameter estimation of a multinomial logistic regression model

In the multinomial regression model, we consider the methodology for simultaneous model selection and parameter estimation by using the shrinkage and LASSO (least absolute shrinkage and selection operation) [R. Tibshirani, Regression shrinkage and selection via the LASSO, J. R. Statist. Soc. Ser. B 58 (1996), pp. 267–288] strategies. The shrinkage estimators (SEs) provide significant improvement over their classical counterparts in the case where some of the predictors may or may not be active for the response of interest. The asymptotic properties of the SEs are developed using the notion of asymptotic distributional risk. We then compare the relative performance of the LASSO estimator with two SEs in terms of simulated relative efficiency. A simulation study shows that the shrinkage and LASSO estimators dominate the full model estimator. Further, both SEs perform better than the LASSO estimators when there are many inactive predictors in the model. A real-life data set is used to illustrate the suggested shrinkage and LASSO estimators.     

Estimation and selection procedures in regression: An L1 approach

The authors consider the problem of estimating a regression function go involving several variables by the closest functional element of a prescribed class _G that is closest to it in the L₁ norm. They propose a new estimator ? based on independent observations and give explicit finite sample bounds for the L₁distance between ?g and go. They apply their estimation procedure to the problem of selecting the smoothing parameter in nonparametric regression.     

Quantile estimation and comparing two independent groups with an approach based on percentile bootstrap

Although the most common approach for comparing two independent groups is on the basis of some measure of location, determination of the differences in the tails of the groups is often of interest. In this study, Harrell–Davis estimator, Sfakianakis–Verginis estimators and default quantile estimator of R are used in conjunction with a percentile bootstrap method with the aim of comparing two independent groups via the quantiles, and the relative efficiencies of Harrell–Davis and Sfakianakis–Verginis estimators are compared. General performance of Sfakianakis–Verginis estimators was much better than Harrell–Davis estimator in terms of both saving actual type I error and relative efficiency.     

Spatial Matérn Fields Driven by Non‐Gaussian Noise

The article studies non‐Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is on non‐Gaussian random fields with Matérn covariance functions, and in particular, we show how the SPDE formulation of a Laplace moving‐average model can be used to obtain an efficient simulation method as well as an accurate parameter estimation technique for the model. This should be seen as a demonstration of how these techniques can be used, and generalizations to more general SPDEs are readily available.