Error variance estimation via least squares for small sample nonparametric regression

In this paper we explore statistical properties of some difference-based approaches to estimate an error variance for small sample based on nonparametric regression which satisfies Lipschitz condition. Our study is motivated by Tong and Wang (2005), who estimated error variance using a least squares approach. They considered the error variance as the intercept in a simple linear regression which was obtained from the expectation of their lag-k Rice estimator. Their variance estimators are highly dependent on the setting of a regressor and weight of their simple linear regression. Although this regressor and weight can be varied based on the characteristic of an unknown nonparametric mean function, Tong and Wang (2005) have used a fixed regressor and weight in a large sample and gave no indication of how to determine the regressor and the weight. In this paper, we propose a new approach via local quadratic approximation to determine this regressor and weight. Using our proposed regressor and weight, we estimate the error variance as the intercept of simple linear regression using both ordinary least squares and weighted least squares. Our approach applies to both small and large samples, while most existing difference-based methods are appropriate solely for large samples. We compare the performance of our approach with other existing approaches using extensive simulation study. The advantage of our approach is demonstrated using a real data set.     

Change point test of tail index for autoregressive processes

In this paper, we extend the change point test for tail index proposed by Quintos, Fan, and Phillips (2001) to that based on autoregressive residuals. It is shown that the asymptotic null distribution of the test remains the same as that of the version in i.i.d. samples. A simulation study is carried out for illustration.     

The rights of the child enabling community development to contribute to a valid social work practice with children at risk

This paper presents a way of thinking about and doing child protection work using community development (CD) principles to guide practice. It suggests that a useful addition to CD can be found within the rights of the child provisions in Human Rights conventions. Using examples from the authors' three countries to illustrate the work that practitioners do in their work with children at risk, we argue that social work practice can be enhanced by the inclusion of these principles and practices which are essentially core generic social work practice. However, much of social work with the protection of children is bound by ‘risk’ perceptions which result in investigatory approaches being used as a first action, often to the exclusion of preventive approaches. This article demonstrates that in very different situations from different environments, CD in concert with the principles of the rights of the child can assist good outcomes with children at risk. A model is presented for unifying the worldview of human/children's rights with social work's core concern, the protection of children, using generic social work skills.     

Hierarchical Bayesian Approach to a Multi-Site Hidden Markov Model

Multivariate data with a sequential or temporal structure occur in various fields of study. The hidden Markov model (HMM) provides an attractive framework for modeling long-term persistence in areas of pattern recognition through the extension of independent and identically distributed mixture models. Unlike in typical mixture models, the heterogeneity of data is represented by hidden Markov states. This article extends the HMM to a multi-site or multivariate case by taking a hierarchical Bayesian approach. This extension has many advantages over a single-site HMM. For example, it can provide more information for identifying the structure of the HMM than a single-site analysis. We evaluate the proposed approach by exploiting a spatial correlation that depends on the distance between sites.     

Preeradication Vaccine Policy Options for Poliovirus Infection and Disease Control

With the circulation of wild poliovirus (WPV) types 1 and 3 continuing more than a decade after the original goal of eradicating all three types of WPVs by 2000, policymakers consider many immunization options as they strive to stop transmission in the remaining endemic and outbreak areas and prevent reintroductions of live polioviruses into nonendemic areas. While polio vaccination choices may appear simple, our analysis of current options shows remarkable complexity. We offer important context for current and future polio vaccine decisions and policy analyses by developing decision trees that clearly identify potential options currently used by countries as they evaluate national polio vaccine choices. Based on a comprehensive review of the literature we (1) identify the current vaccination options that national health leaders consider for polio vaccination, (2) characterize current practices and factors that appear to influence national and international choices, and (3) assess the evidence of vaccine effectiveness considering sources of variability between countries and uncertainties associated with limitations of the data. With low numbers of cases occurring globally, the management of polio risks might seem like a relatively low priority, but stopping live poliovirus circulation requires making proactive and intentional choices to manage population immunity in the remaining endemic areas and to prevent reestablishment in nonendemic areas. Our analysis shows remarkable variability in the current national polio vaccine product choices and schedules, with combination vaccine options containing inactivated poliovirus vaccine and different formulations of oral poliovirus vaccine making choices increasingly difficult for national health leaders.     

Diabetes mellitus in older men

Most persons with diabetes mellitus are over the age of 60 years. Males develop diabetes more commonly than females. Older diabetics tend to have both impaired insulin release as well as insulin resistance. In older persons diabetes mellitus is associated with decreased functional status and cognitive dysfunction. In general, older persons with diabetes are inclined to be underdiagnosed and undertreated. Managing diabetes in older persons requires special considerations because of their differences in pathophysiology of diabetes and strong association with functional, cognitive impairments and comorbidities. The use of strict therapeutic diets is not recommended in older persons. Treatment of hypertension and hyperglycemia can improve outcomes in older persons. The interdisciplinary team approach is important for care of older diabetic persons.     

A note on the differentiation formula in Stratonovich type for fractional Brownian sheet

We consider a new proof on the differentiation formula in Stratonovich type for fractional Brownian sheet. Our proof is based on the repeated applications of differentiation formulas in Stratonovich form for a one-parameter Gaussian process.     

Development of life-test sampling plans for exponential distributions based on accelerated life testing

This paper presents a procedure for developing life-test sampling plans for exponential distributions based upon accelerated life testing(ALT). Type II censoring is assumed at each overstress level. The derived test statistic is shown to be a quotient of two independent random variables, each of which is a rational power of a Chi-square random variable. The distribution of the test statistic is characterized by the H-function, which can be numerically evaluated to obtain desired sampling plans.