On bagging and nonlinear estimation

We propose an elementary model for the way in which stochastic perturbations of a statistical objective function, such as a negative log-likelihood, produce excessive nonlinear variation of the resulting estimator. Theory for the model is transparently simple, and is used to provide new insight into the main factors that affect performance of bagging. In particular, it is shown that if the perturbations are sufficiently symmetric then bagging will not significantly increase bias; and if the perturbations also offer opportunities for cancellation then bagging will reduce variance. For the first property it is sufficient that the third derivative of a perturbation vanish locally, and for the second, that second and fourth derivatives have opposite signs. Functions that satisfy these conditions resemble sinusoids. Therefore, our results imply that bagging will reduce the nonlinear variation, as measured by either variance or mean-squared error, produced in an estimator by sinusoid-like, stochastic perturbations of the objective function. Analysis of our simple model also suggests relationships between the results obtained using different with-replacement and without-replacement bagging schemes. We simulate regression trees in settings that are far more complex than those explicitly addressed by the model, and find that these relationships are generally borne out.     

Occupational Advantage and the Impact of College Rank on Labor Market Outcomes*

Most analyses of the effects of college rank on labor market outcomes focus on its average impact across sub-populations and employment situations. The framework adopted in this paper, however, suggests that the effects of college rank may vary by individual characteristics and type of job. Using data from the 1973 Occupational Changes in a Generation Survey, we test three hypotheses suggesting that occupational advantage, as measured either by family of origin or current position, is a significant determinant of capacity to convert increments in college prestige into labor market success. The findings suggest that where one went to college is especially consequential for (1) the occupational status of individuals from professional families; (2) the earnings of individuals from both professional and managerial families; and (3) the earnings of individuals in both professional and managerial positions. Overall, these findings tend to confirm the study's underlying hypothesis that aggregate analyses of college rank may be misleading when applied across sub-populations and employment situations.     

An Analysis of the Uncertainties in Estimates of Radon-Induced Lung Cancer

A recent report by the National Academy of Sciences estimates that the radiation dose to the bronchial epithelium, per working level month (WLM) of radon daughter exposure, is about 30% lower for residential exposures than for exposures received in underground mines. Adjusting the previously published BEIR IV radon risk model accordingly, the unit risk for indoor exposures of the general population is about 2.2 x 10(-4) lung cancer deaths (lcd)/WLM. Using results from EPA's National Residential Radon Survey, the average radon level is estimated to be about 1.25 pCi/L, and the annual average exposure about 0.242 WLM. Based on these estimates, 13,600 radon-induced lcd/yr are projected for the United States. A quantitative uncertainty analysis was performed, which considers: statistical uncertainties in the epidemiological studies of radon-exposed miners; the dependence of risk on age at, and time since, exposure; the extrapolation of risk estimates from mines to homes based on comparative dosimetry; and uncertainties in the radon daughter levels in homes and in the average residential occupancy. Based on this assessment of the uncertainties in the unit risk and exposure estimates, an uncertainty range of 7000-30000 lcd/yr is derived.     

The Culture of Poverty and Learned Helplessness: A Social Psychological Perspective*

This paper links the sociological work of Ball on the analgesic subculture-a subculture of Appalachian poverty-with the sociological research of Merton on adaptation, the social psychological research of Seeman on alienation, and the psychological research of Seligman on learned helplessness. We suggest that (1) Ball's cultural explanation work has not been pursued because it has not been integrated with relevant structural and relevant psychological theory and (2) the analgesic subculture of Appalachia is an extreme intensification of the consequences of alienation resulting in a psychology of learned helplessness.     

Children of Gamblers Anonymous members

One hundred and five children of Gamblers Anonymous (GA) members and pathological gamblers in treatment were surveyed concerning behavioral, psychological, and emotional problems as well as parental use of violence. The results were compared with control groups and Jacobs' study of high school students who reported they were children of compulsive gamblers. Children of known pathological gamblers were less likely to admit to moderate or heavy use of cocaine/crack and less likely to gamble more than they could afford than either Jacobs' children of compulsive gamblers or controls. Children of pure gamblers looked more like Jacobs' controls than the self-reported children of compulsive gamblers he surveyed on several measures. Children of multiple-problem families are more likely than children of pure gamblers to smoke tobacco, get drunk, overeat, sleep worse than most people, have an unhappy present state of mind, and feel more insecure, inferior, or inadequate than most. GA and treatment children as a whole were more likely to say they had an unhappy childhood, and feel a need for success, acceptance, and approval than Jacobs' children of compulsive gamblers or his controls. Using Strauset al.'s conflict tactics scale, children of known pathological gamblers were more subject to parental violence and abuse than nationally normed samples. On most measures, the children of multiple-problem families fared worse than children of pure gamblers. However, there were no differences in the expressions of anger, hurt, sadness, depression, confusion, and other feelings between these groups concerning their parents' gambling. Treatment implications of the findings are discussed.The authors would like to thank Mary Heineman, M.S.W., and Valerie Lorenz, Ph.D., for their comments on an earlier draft of this paper.     

Small Sample Tests for Shape Parameters of Gamma Distributions

The introduction of shape parameters into statistical distributions provided flexible models that produced better fit to experimental data. The Weibull and gamma families are prime examples wherein shape parameters produce more reliable statistical models than standard exponential models in lifetime studies. In the presence of many independent gamma populations, one may test equality (or homogeneity) of shape parameters. In this article, we develop two tests for testing shape parameters of gamma distributions using chi-square distributions, stochastic majorization, and Schur convexity. The first one tests hypotheses on the shape parameter of a single gamma distribution. We numerically examine the performance of this test and find that it controls Type I error rate for small samples. To compare shape parameters of a set of independent gamma populations, we develop a test that is unbiased in the sense of Schur convexity. These tests are motivated by the need to have simple, easy to use tests and accurate procedures in case of small samples. We illustrate the new tests using three real datasets taken from engineering and environmental science. In addition, we investigate the Bayes’ factor in this context and conclude that for small samples, the frequentist approach performs better than the Bayesian approach.     

Estimates of trade-related adjustment costs in Syria

The scope and complexity of international trading arrangements in the Middle East, as well as their spotty historical record of success, underscore the urgent need for an adequate understanding of the relative costs and benefits of participation in preferential trading arrangements and, more generally, of changes in the domestic import regimes. This paper seeks to address this problem by providing estimates of the adjustment costs associated with two broad classes of hypothetical trade policy scenarios for Syria: participation in the proposed EU-Syria Association Agreement, and border tax-related changes affecting the domestic import regime. We find that the revenue consequences of the first scenario are likely to be low if an appropriate stepwise implementation of the agreement can be ensured; our analysis of the second scenario suggests that all border taxes can be eliminated, and the number of tariff bands reduced, while ensuring revenue neutrality, if a VAT of a reasonable size is introduced.     

Comparison op some two sample tests for equality of variances

The F-test, F max-test and Bartlett's test are compared on the basis of power for the purpose of testing the equality of variances in two normal populations. The power of each test is expressed as a linear combination of F-probabilities. Bartlett's test is noted to be unbiased, UMPU, consistent against all alterna¬tives and the test which yields minimum length confidence intervals on the ratio of the variancesλ=σ₁ ² /σ² ₂ The two samples Bartlett critical values, although not recognized as such, are found in the works of other authors. Tables of the powers of each test are given for various values of λ, levels of significance a and the respective sample sizes, n₁ and n₂.     

Comments on estimators based on error in the predicted distribution function

In estimation of percentiles in the exponential distribution, the distribution function evaluated at the estimated percentile is often evaluated for purposes of warranty considerations. Optimal estimators are discussed and compared on their error in the predicted distribution function. Inconsistency is shown to exist between measures of closeness and measures of risk in the predicted distribution function. An optimal estimator based on absolute loss in the predicted distribution function is obtained and shown to be superior in measures of closeness to the optimal estimator, which minimizes squared error loss in the predicted distribution function.