Diagnostics for elliptical linear mixed models with first-order autoregressive errors

For longitudinal time series data, linear mixed models that contain both random effects across individuals and first-order autoregressive errors within individuals may be appropriate. Some statistical diagnostics based on the models under a proposed elliptical error structure are developed in this work. It is well known that the class of elliptical distributions offers a more flexible framework for modelling since it contains both light- and heavy-tailed distributions. Iterative procedures for the maximum-likelihood estimates of the model parameters are presented. Score tests for the presence of autocorrelation and the homogeneity of autocorrelation coefficients among individuals are constructed. The properties of test statistics are investigated through Monte Carlo simulations. The local influence method for the models is also given. The analysed results of a real data set illustrate the values of the models and diagnostic statistics.     

Prevalence,incidence and risk factors of testosterone deficiency in a population-based cohort of men: results from the study of health in Pomerania

Objective.?Low total testosterone levels (TT) have been associated with increased morbidity and mortality. However, the prevalence and incidence of testosterone deficiency (TD) in association with its risk has not been assessed systematically to date.

Methods.?Data from the prospective population-based Study of Health in Pomerania were used. From the 2117 men aged 20–79 years at baseline, 1490 men with complete TT data were analysed. Crude and age-specific prevalence and incidence rates of TD were estimated by TT levels below the age-specific 10th percentile. Analysis of covariance and Poisson regression models were used to assess the association of socio-demographic characteristics, health-related lifestyle, as well as somatometric, medical and laboratory measures with risk of incident TD.

Results.?TD baseline prevalence was 10.4% (N?=?155) and incidence 11.7 per 1000 person-years. TT levels showed a significant age-related decline with an unadjusted rate of 0.05 nmol/l per year. Obesity, metabolic syndrome, diabetes and dyslipidaemia were identified as risk factors of incident TD. Subpopulations of men without the revealed risk factors at both examinations maintained constant TT levels over time.

Conclusions.?Besides aging alone, lifestyle and different comorbidities were associated with TT level decline, suggesting that the age-related TT decline may be at least partly prevented through the management of potentially modifiable risk factors and health related behaviour.     

Exact likelihood inference for Laplace distribution based on Type-II censored samples

We develop exact inference for the location and scale parameters of the Laplace (double exponential) distribution based on their maximum likelihood estimators from a Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Upon conditioning first on the number of observations that are below the population median, exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of these pivotal quantities. Tables of quantiles are presented for the complete sample case.     

Unbiastld estimation of parametric functions in sampling from two two-truncation parameter families

We consider the problem of UMVU estimation of a U-estimable function of four unknown truncation parameters based on two independent random samples from two two-truncation parameter families. In particular, we obtain the UMVU estimator of functional, P (Y > X). Also the confidence intervals for some parametric functions are obtained.     

Planning for the 1950 Censuses of Population and Agriculture

The change from the z of “Student's” 1908 paper to the t of present day statistical theory and practice is traced and documented. It is shown that the change was brought about by the extension of “Student's” approach, by R.A. Fisher, to a broader class of problems, in response to a direct appeal from “Student” for a solution to one of these problems.     

Parameter estimation in nonlinear regression models 1

Fisher information contained in record values, inter-record times and their concomitants from a sample of fixed size is derived in general and explicit expressions are deduced for some specific known bivariate classes of distributions. A comparison between fixed sampling and inverse sampling schemes with equal number of records and concomitants is also carried out. We also consider parameter estimation based on bivariate records and a small simulation study is done.     

Geometric sample size determination in Bayesian analysis

The problem of sample size determination in the context of Bayesian analysis is considered. For the familiar and practically important parameter of a geometric distribution with a beta prior, three different Bayesian approaches based on the highest posterior density intervals are discussed. A computer program handles all computational complexities and is available upon request.     

On shrinkage m-estimators of location parameters

For a general class of continuous ( and marginally symmetric ) inultivariate distributions, based on suitable M-statistics ( involving bounded but possibly discontinuous score generating functions), shrinkage estimators of location are considered. These estimators are based on the James-Stein type rule and incorporates the idea of preliminary test estimation too. The main emphasis is laid on the study of asymptotic tdistributional ) risk properties of these est-innators, and asymptotic tin-) adraissibility results are also studied under fairly general regularity conditions.     

说“魃(八)怪”

问题 ,不失为一种有效至少是可行的办法 ,这与化验报告作为医生诊断疾病的参考或依据同属一理。举两个例子。例子一 :据笔者研究 ,《红楼梦》前 80回的语言有不少江淮方言 (下江官话 )的成份 (见《〈红楼梦〉语言的地方色彩》 ,载《红楼梦学刊》1 984年第 2辑 ) ,表明曹雪芹谙熟扬州、南京方言 ;而红学界对雍正六年 ( 1 72 8年 )曹家举家北返时曹雪芹的年龄有两种说法 ,一为 5岁 ,一为1 3岁 ,对《红楼梦》中方言的研究则支持后一说法。———如果孩提时代就离开一个地方 ,该地方言的影响就不可能有那么大了。又 ,后 40回和前80回运用方言情…     

Terrorist Population Dynamics Model

A system that includes a number of terrorist cells is considered. The cells can consist of one or more terrorists. The current number of terrorist cells is further denoted by N(t), where t is a current time counted from any appropriate origin. The objective is to find the evolution of the system in terms of N(t) and some interpretable parameters, such as the initial number of the terrorist cells N0=N(0), the cell disabling rate constant lambda (or the cell half-life t1/2), and the rate of formation of new cells P. The cost-effectiveness analysis, performed in the framework of the model, reveals that the effectiveness of disabling a terrorist cell is getting worse after 2-3 half-lives of a cell, which shows that if the anti-terrorist actions have not reached their goal during that time, the respective policy should be considered for revision, using the risk assessment consideration. Another important issue raised concerns balancing the efforts related to counterterrorism actions inside the system and the efforts protecting its borders. The respective data analysis is suggested and illustrated using simulated data.