A semiparametric estimator of the distribution function of a variable measured with error

The estimation of the distribution functon of a random variable X measured with error is studied. Let the i-th observation on X be denoted by Y_iX_i+ε_i where ε_i is the measuremen error. Let {Y_i} (i=1,2,…,n) be a sample of independent observations. It is assumed that {X_i} and {∈_i} are mutually independent and each is identically distributed. As is standard in the literature for this problem, the distribution of e is assumed known in the development of the methodology. In practice, the measurement error distribution is estimated from replicate observations.

The proposed semiparametric estimator is derived by estimating the quantises of X on a set of n transformed V-values and smoothing the estimated quantiles using a spline function. The number of parameters of the spline function is determined by the data with a simple criterion, such as AIC. In a simulation study, the semiparametric estimator dominates an optimal kernel estimator and a normal mixture estimator for a wide class of densities.

The proposed estimator is applied to estimate the distribution function of the mean pH value in a field plot. The density function of the measurement error is estimated from repeated measurements of the pH values in a plot, and is treated as known for the estimation of the distribution function of the mean pH value.     

Business Education: Real Time or Semester Time?

Both the context and content of management education are changing as new providers compete for market share. As education goes increasingly online and offcampus, many traditional universities will feel the effects of consolidation within their own ranks. Business schools will face additional pressure as corporate universities and Internet universities offer an economical and effective means of professional education. Unless MBA programs seize opportunities for creative collaboration, today’s potential partners will become tomorrow’s predators. This revised version was published online in July 2006 with corrections to the Cover Date.     

Potency Factors for Risk Assessment at Libby,Montana

We reanalyzed the Libby vermiculite miners’ cohort assembled by Sullivan to estimate potency factors for lung cancer, mesothelioma, nonmalignant respiratory disease (NMRD), and all‐cause mortality associated with exposure to Libby fibers. Our principal statistical tool for analyses of lung cancer, NMRD, and total mortality in the cohort was the time‐dependent proportional hazards model. For mesothelioma, we used an extension of the Peto formula. For a cumulative exposure to Libby fiber of 100 f/mL‐yr, our estimates of relative risk (RR) are as follows: lung cancer, RR = 1.12, 95% confidence interval (CI) =[1.06, 1.17]; NMRD, RR = 1.14, 95% CI =[1.09, 1.18]; total mortality, RR = 1.06, 95% CI =[1.04, 1.08]. These estimates were virtually identical when analyses were restricted to the subcohort of workers who were employed for at least one year. For mesothelioma, our estimate of potency is K_M = 0.5 × 10^?8, 95% CI =[0.3 × 10^?8, 0.8 × 10^?8]. Finally, we estimated the mortality ratios standardized against the U.S. population for lung cancer, NMRD, and total mortality and obtained estimates that were in good agreement with those reported by Sullivan. The estimated potency factors form the basis for a quantitative risk assessment at Libby.     

A note on the randomized response technique

It is pointed out that the usual estimators for the parameters of a randomized response model are not, contrary to popular belief, maximum likelihood estimators.     

Impaired angiogenesis in the aged

The process of angiogenesis, during which new blood vessels are formed, is impaired during aging. This Perspective describes many of the myriad components of the angiogenic response that are altered with age. In addition, the impact of impaired angiogenesis on wound healing, vascular disease, and cancer in the aged is discussed.     

The pursuit of socially modifiable contingencies in mental health

The effort to understand the meanings of the well-demonstrated linkages between mental health and one's locations in the social structure has commanded a great deal of research attention over the past half century. Following a brief consideration of my early efforts to make a contribution in this regard, some recent and ongoing work is summarized. In concert with important work by others, these findings support the conclusion that differences in exposure to social stress represent a much more critical contingency in mental health and substance use outcomes than has generally been assumed. In addition, reported results indicate that the lifetime experience of multiple adversities is quite common among young people in South Florida and, presumably, elsewhere and the likelihood that the compelling linkage observed between cumulative adversity and risk for psychiatric and substance disorders is causal in nature. It is suggested that the development of interventions in the service of stress prevention or reduction should command a greater proportion of the attention of researchers and interventionists.