On the trimmed mean and minimax-variance L-estimation in Kolmogorov neighbourhoods

We consider the properties of the trimmed mean, as regards minimax-variance L-estimation of a location parameter in a Kolmogorov neighbourhood K() of the normal distribution: We first review some results on the search for an L-minimax estimator in this neighbourhood, i.e. a linear combination of order statistics whose maximum variance in K_t() is a minimum in the class of L-estimators. The natural candidate – the L-estimate which is efficient for that member of K_t,() with minimum Fisher information – is known not to be a saddlepoint solution to the minimax problem. We show here that it is not a solution at all. We do this by showing that a smaller maximum variance is attained by an appropriately trimmed mean. We argue that this trimmed mean, as well as being computationally simple – much simpler than the efficient L-estimate referred to above, and simpler than the minimax M- and R-estimators – is at least “nearly” minimax.     

Quantifying the Distribution of Inhalation Exposure in Human Populations: 2. Distributions of Time Spent by Adults, Adolescents, and Children at Home, at Work, and at School

Using distributions of time spent at various ventilation levels, ranges of inhalation exposure in the population can be established. Distributions of exposure time were determined using results of a study by the California Air Resources Board (CARB) which focused on time spent by humans participating in various activities and the locations where the activities occurred. The daily at-home activities from the CARB study were assigned to one of three ventilation levels, generating aggregate time periods. Distinct age and gender populations were identified, and distributions for aggregate time were established for these populations at each of the ventilation levels. In addition to aggregate time spent at home, distributions for various ages and genders were established for aggregate time spent at school and work. By combining distributions of aggregate time with corresponding ventilation rates, the distribution of inhalation rates can be established for at home, at work, and at school exposures.     

Cybersex: The Impact of a Contemporary Problem on the Practices of Marriage and Family Therapists

The number of people accessing the Internet for sexual purposes (cybersex) has increased dramatically over the last 10 years. However, little research has been conducted to determine how frequently clients present for treatment with cybersex‐related issues. One hundred sixty‐four clinical members of the American Association for Marriage and Family Therapy participated in the current study, which was conducted to identify the impacts of cybersex on MFTs’ practices. Most respondents report seeing clients with cybersex‐related issues, with client numbers increasing over the past 2 years. Although most respondents felt prepared to diagnose and treat adults with cybersex problems, half felt unprepared to diagnose and treat children. Lastly, most respondents reported that their required college courses were not helpful in preparing them to diagnose and treat cybersex‐related problems. The implications of study findings are discussed.     

Physical distribution: A suitable case for treatment

Physical distribution is a key, but neglected, function of business. Yet it is an area which offers tremendous opportunities for cost reduction, improved efficiency and better customer service. All these can contribute to increased profitability. Finding the means to achieve these improvements need not be a daunting task or one which requires sophisticated techniques. This article shows how ordinary solutions can be found and implemented by ordinary companies; how physical distribution should take its place as the important cost centre that it is; and the four major areas where cost savings can be most readily effected.     

Bayesian inference and model comparison for asymmetric smooth transition heteroskedastic models

Inference, quantile forecasting and model comparison for an asymmetric double smooth transition heteroskedastic model is investigated. A Bayesian framework in employed and an adaptive Markov chain Monte Carlo scheme is designed. A mixture prior is proposed that alleviates the usual identifiability problem as the speed of transition parameter tends to zero, and an informative prior for this parameter is suggested, that allows for reliable inference and a proper posterior, despite the non-integrability of the likelihood function. A formal Bayesian posterior model comparison procedure is employed to compare the proposed model with its two limiting cases: the double threshold GARCH and symmetric ARX GARCH models. The proposed methods are illustrated using both simulated and international stock market return series. Some illustrations of the advantages of an adaptive sampling scheme for these models are also provided. Finally, Bayesian forecasting methods are employed in a Value-at-Risk study of the international return series. The results generally favour the proposed smooth transition model and highlight explosive and smooth nonlinear behaviour in financial markets.     

New balanced sampling plans excluding adjacent units

Hedayat et al. [1988a. Sampling plans excluding contiguous units. J. Statist. Plann. Inference 19, 159–170; 1988b. Designs in survey sampling avoiding contiguous units. In: Krishnaiah, P.R., Rao, C.R. (Eds.). Handbook of Statistics, vol. 6. Elsevier, Amsterdam, pp. 575–583] first introduced balanced sampling designs for the exclusion of contiguous units. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. There remain many open questions about the existence of such plans and their extension to plans excluding adjacent units. We present new generation techniques and new balanced sampling plans for the exclusion of adjacent units under finite, one-dimensional, circularly and linearly ordered populations.     

Profits and incentive compensation in nonprofit firms

Incentive contracts based on profit sharing, cost reduction, or other measures of performance no longer need to endanger a nonprofit firm's tax exemption; such measures have been urged for adoption in the nonprofit sector. However, the nonprofit differs from the for-profit sector in that contracts have side effects on the solicitation and offering of donations and on the character of those who choose to work in the nonprofit sector. In addition, it is more difficult in the nonprofit sector to obtain an appropriate output measure for use in calculating bonuses.     

Transformations for Smooth Regression Models with Multiplicative Errors

We consider whether one should transform to estimate nonparametrically a regression curve sampled from data with a constant coefficient of variation, i.e. with multiplicative errors. Kernel-based smoothing methods are used to provide curve estimates from the data both in the original units and after transformation. Comparisons are based on the mean-squared error (MSE) or mean integrated squared error (MISE), calculated in the original units. Even when the data are generated by the simplest multiplicative error model, the asymptotically optimal MSE (or MISE) is surprisingly not always obtained by smoothing transformed data, but in many cases by directly smoothing the original data. Which method is optimal depends on both the regression curve and the distribution of the errors. Data-based procedures which could be useful in choosing between transforming and not transforming a particular data set are discussed. The results are illustrated on simulated and real data.     

Random regression models for human immunodeficiency virus ribonucleic acid data subject to left censoring and informative drop-outs

Objectives in many longitudinal studies of individuals infected with the human immunodeficiency virus (HIV) include the estimation of population average trajectories of HIV ribonucleic acid (RNA) over time and tests for differences in trajectory across subgroups. Special features that are often inherent in the underlying data include a tendency for some HIV RNA levels to be below an assay detection limit, and for individuals with high initial levels or high ranges of change to drop out of the study early because of illness or death. We develop a likelihood for the observed data that incorporates both of these features. Informative drop-outs are handled by means of an approach previously published by Schluchter. Using data from the HIV Epidemiology Research Study, we implement a maximum likelihood procedure to estimate initial HIV RNA levels and slopes within a population, compare these parameters across subgroups of HIV-infected women and illustrate the importance of appropriate treatment of left censoring and informative drop-outs. We also assess model assumptions and consider the prediction of random intercepts and slopes in this setting. The results suggest that marked bias in estimates of fixed effects, variance components and standard errors in the analysis of HIV RNA data might be avoided by the use of methods like those illustrated.