Testing and Estimating Shape-Constrained Nonparametric Density and Regression in the Presence of Measurement Error

In many applications we can expect that, or are interested to know if, a density function or a regression curve satisfies some specific shape constraints. For example, when the explanatory variable, X, represents the value taken by a treatment or dosage, the conditional mean of the response, Y , is often anticipated to be a monotone function of X. Indeed, if this regression mean is not monotone (in the appropriate direction) then the medical or commercial value of the treatment is likely to be significantly curtailed, at least for values of X that lie beyond the point at which monotonicity fails. In the case of a density, common shape constraints include log-concavity and unimodality. If we can correctly guess the shape of a curve, then nonparametric estimators can be improved by taking this information into account. Addressing such problems requires a method for testing the hypothesis that the curve of interest satisfies a shape constraint, and, if the conclusion of the test is positive, a technique for estimating the curve subject to the constraint. Nonparametric methodology for solving these problems already exists, but only in cases where the covariates are observed precisely. However in many problems, data can only be observed with measurement errors, and the methods employed in the error-free case typically do not carry over to this error context. In this paper we develop a novel approach to hypothesis testing and function estimation under shape constraints, which is valid in the context of measurement errors. Our method is based on tilting an estimator of the density or the regression mean until it satisfies the shape constraint, and we take as our test statistic the distance through which it is tilted. Bootstrap methods are used to calibrate the test. The constrained curve estimators that we develop are also based on tilting, and in that context our work has points of contact with methodology in the error-free case.     

Quantifying the costs of drought: new evidence from life satisfaction data

We estimate the cost of droughts by matching rainfall data with individual life satisfaction. Our context is Australia over the period 2001 to 2004, which included a particularly severe drought. Using fixed-effect models, we find that a drought in spring has a detrimental effect on life satisfaction equivalent to an annual reduction in income of A$18,000. This effect, however, is only found for individuals living in rural areas. Using our estimates, we calculate that the predicted doubling of the frequency of spring droughts will lead to the equivalent loss in life satisfaction of just over 1% of GDP annually.

AN ALTERNATING LEAST-SQUARES PROCEDURE FOR ESTIMATING MISSING PREFERENCE DATA IN PRODUCT-CONCEPT TESTING*

Product-concept testing is a popular activity in marketing research. Often the number of new product/service concepts under study far exceeds the time available for any single respondent. Respondents therefore may receive only a subset of the concepts comprising the total design. Researchers are interested in making plausible imputations for the missing evaluations of any given respondent. This paper proposes a model and an iterative estimation procedure to impute missing entries for each evaluator. The model and the procedure incorporate (1) the internal structure of the response matrix and (2) an ancillary matrix of (nonmissing) respondent background data; they also (3) allow for individual differences in respondents' uses of the numerical rating scale. The model is applied to both real and synthetic data. Suggestions also are given on how the data imputations may be used in market segmentation and product-line decisions.     

A survey of fruit machine gambling in adolescents

Fruit machine gambling among children and young people in the United Kingdom has attracted increasing interest. Since 1985 a number of questionnaire surveys have been conducted attempting to assess the incidence of adolescent fruit machine use and to explore its relationship with delinquency. Data yielded by these surveys have been somewhat inconsistent. Estimates of the prevalence of fruit machine gambling have varied considerably and there is disagreement over its association with deviant behaviour. Researchers have drawn divergent conclusions with different implications for legislation. In the present study, questionnaires were administered to 1,395 11–12 year old and 14–15 year old school children in the Birmingham area. Although for the majority, fruit machine gambling was found to be an infrequent activity involving fairly small amounts of money, a small but significant proportion were found to be gambling often and spending in excess of their income. There was also evidence to suggest that arcades may serve as venues for undesirable activities.This research was funded by the Church of England Children's Society and the authors gratefully acknowledge their support.The authors acknowledge their special thanks to William Wyatt for his continued assistance throughout this project.     

A first generation critic comes of age: Reflections of a critical gerontologist

This paper reflects upon the direction and evolution of my scholarly endeavors as a sociologist of four decades in the field of aging, with thoughts on the future direction of this work and the challenges for the larger field. The perspective presented is located within two frameworks of active debate: the sociology of knowledge(s) [Gouldner, A. 1970. The Coming Crisis of Western Sociology. New York: Basic Books] and public sociology, which is one of the four major types of sociology identified by Burawoy [Burawoy, M. (2005, 2007). A call for public sociology. In D. Clawson, R. Zussman, J. Misra, N. Gerstel, R. Stokes, & R. L. Anderton (Eds.), Public Sociology. Berkeley: University of California Press.], also including traditional professional sociology, policy sociology, and critical sociology.