The estimation of derivatives of a nonparametric regression function when the data are correlated

A kernel estimator of a derivative of arbitrary order of a nonparametric average population curve is considered for a correlated-errors model with balanced replicate measurements at each design point. Asymptotic expansions of the mean squared error are derived for two classes of correlation functions in the model. Consistency, choice of smoothing parameter, and rates of convergence are examined for the important special cases of estimating the first and second derivatives.     

Empowering Community-Based Programs for Youth Development

This article discusses the need for community-based programs for youth and their families and urges the social work profession to resume its historical leadership in such programs while incorporating recent theory and practice. The authors describe the reasons why social workers abandoned neighborhood-based youth development services, the intended outcomes of such services, and current societal and professional trends that support a revival of social work’s involvement in youth development. They discuss one school of social work’s current participation in a youth agency partnership and examine implications of the suggested revival for social work education. Collaboration among families, schools, diverse community services, agencies, and educators is emphasized.     

Volunteerism and Social Work Educators: Findings from a National Survey

Abstract

This study reports the results of a national survey designed to identify the nature and levels of volunteer work that social work educators contribute to the social welfare sector. Findings reveal that nearly all social work educators engage in formal volunteer work and perform a variety of roles in human service agencies. The most common volunteer activities are advocacy, administration and consultation. The least common volunteer activities are evaluation, data management and emergency services. Study results also indicate that tenure status and primary teaching area are positively associated with the amount and type of volunteer work performed.     

Expected absolute departure of chi-square from its median

We develop a formula for the expected absolute departure of x² from its median.     

Screening procedures using quadratic forms

In quality control, a performance variable having a two-sided specification limit is common for assessing lot quality. Sometimes it is difficult or impossible to measure the performance variable directly; for example, when testing is destructive, expensive, or when the performance variable is related to the lifetime of the product. However, it may happen that there are several concomitant variables which are easily measured and which correlate highly with the variable of interest. Thus, one may use measurements on these variables to select or screen product which will have a high conditional probability of meeting product specification. We consider this situation when all variables have a joint multivariate normal distribution and the specification limits on the performance variable are two-sided.     

Kernel estimation of a distribution function

A distribution function is estimated by a kernel method with

a poinrwise mean squared error criterion at a point x. Relation- ships between the mean squared error, the point x, the sample size and the required kernel smoothing parazeter are investigated for several distributions treated by Azzaiini (1981). In particular it is noted that at a centre of symmetry or near a mode of the distribution the kernei method breaks down. Point- wise estimation of a distribution function is motivated as a more useful technique than a reference range for preliminary medical diagnosis.     

Letters to the editor

Relatively little attention has been paid to the use and importance of labels used by men who have sex with men to describe insertive or receptive sexual behavior during intercourse. This study examines sexual self‐labels, sexual behavior, HIV transmission risk, and psychological functioning among 205 HIV‐seropositive men who have sex with men. The majority of participants (88%) identified as a “top, “ a “bottom, “ or “versatile. “ Tops were more likely to engage in insertive anal intercourse than bottoms, and bottoms were more likely to engage in receptive anal intercourse than tops, with versatiles reporting intermediate rates of both behaviors. Although the results suggest preliminary evidence regarding the predictive utility of self‐labels, sexual behaviors of self‐label groups were greatly overlapping. Differences were found among self‐label groups in gay self‐identification, internalized homophobia, sexual sensation seeking, and anxiety. Results suggest an added value in assessing self‐labels in addition to asking about sexual behavior.     

A comparison of various methods for estimating the parameters in mixtures of von mises distributions

In this paper we compare five methods for estimating the unknown parameters in a mixture of two von Mises distributions. We propose a new method based on the characteristic function and compare it with the classical methods based on maximum likelihood and moments. Thus far these methods have been successfully applied only to linear data. Here we show that the application to circular data is reasonably straightforward and that convergence to the final estimates is fairly rapid. For various simulated known mixtures the results obtained are satisfactory. Finally, we introduce a modification of the method of moments which is considerably faster in CPU time than any of the other methods used and gives good results.     

The exact solution to the mle of a decreasing density based on arbitrarily right censored data

Nonparametric maximum likelihood estimation of decreasing and unimodal density functions, based on observations subject to arbitrary right censorship, was considered by McNichols and Padgett(1982). In order to compute their estimators, however, nonlinear equations with linear constraints had to be maximized using numerical techniques. The exact solution to this problem can now be found. An example illustrates the simplicity of the method.     

An emplrical bayes approach in estimating the parameters of the or more geometric distributions

The estimation of the parameters of two or more geometric distribuionsis considered by usinq an empirical Bayesian approach. Robbins (1983) gave empirical Bayes estimates if the number of distributions N is large, buthere we consider the cascwhore N is small. The parameters of the prior distribution areest imated by looking at maximum like lihood and momentest imation methods.