An Investigation of Quantile Function Estimators Relative to Quantile Confidence Interval Coverage

In this article, we investigate the limitations of traditional quantile function estimators and introduce a new class of quantile function estimators, namely, the semi-parametric tail-extrapolated quantile estimators, which has excellent performance for estimating the extreme tails with finite sample sizes. The smoothed bootstrap and direct density estimation via the characteristic function methods are developed for the estimation of confidence intervals. Through a comprehensive simulation study to compare the confidence interval estimations of various quantile estimators, we discuss the preferred quantile estimator in conjunction with the confidence interval estimation method to use under different circumstances. Data examples are given to illustrate the superiority of the semi-parametric tail-extrapolated quantile estimators. The new class of quantile estimators is obtained by slight modification of traditional quantile estimators, and therefore, should be specifically appealing to researchers in estimating the extreme tails.     

Estimation of functions of the parameters of a normal distribution

Several authors have considered the problem of estimating parameters of a distribution after some fixed Gaussian inducing transformation has been applied to the observations. This paper extends this work to the situation where the observations represent a noisy version of a true process, the parameters of the latter requiring estimation     

Comparing mean ranks for repeated measures data

Rank tests are considered that compare t treatments in repeated measures designs. A statistic is given that contains as special cases several that have been proposed for this problem, including one that corresponds to the randomized block ANOVA statistic applied to the rank transformed data. Another statistic is proposed, having a null distribution holding under more general conditions, that is the rank transform of the Hotelling statistic for repeated measures. A statistic of this type is also given for data that are ordered categorical rather than fully rankedo Unlike the Friedman statistic, the statistics discussed in this article utilize a single ranking of the entire sample. Power calculations for an underlying normal distribution indicate that the rank transformed ANOVA test can be substantially more powerful than the Friedman test.     

Concentration Ellipsoids,Their Planes of Support,and the Linear Regression Model

The relationship between the concentration ellipsoid of a random vector and its planes of support is exploited to provide a geometric derivation and interpretation of existing results for a general form of the linear regression model. In particular, the planes of support whose points of tangency to the ellipsoid are contained in the range (or column space) of the design matrix are the source of all linear unbiased minimum variance estimators. The connection between this idea and estimators based on projections is explored, as is also its use in obtaining and interpreting some existing relative efficiency results.     

Construction of Confidence Intervals for the IVIean of a Population Containing Many Zero Values

The likelihood ratio method is used to construct a confidence interval for a population mean when sampling from a population with certain characteristics found in many applications, such as auditing. Specifically, a sample taken from this type of population usually consists of a very large number of zero values, plus a small number of nonzero values that follow some continuous distribution. In this situation, the traditional confidence interval constructed for the population mean is known to be unreliable. This article derives confidence intervals based on the likelihood-ratio-test approach by assuming (1) a normal distribution (normal algorithm) and (2) an exponential distribution (exponential algorithm). Because the error population distribution is usually unknown, it is important to study the robustness of the proposed procedures. We perform an extensive simulation study to compare the percentage of confidence intervals containing the true population mean using the two proposed algorithms with the percentage obtained from the traditional method based on the central limit theorem. It is shown that the normal algorithm is the most robust procedure against many different distributional error assumptions.     

Gibbs sampling for marginal posterior expectations

In earlier work (Gelfand and Smith, 1990 and Gelfand et al, 1990) a sampling based approach using the Gibbs sampler was offered as a means for developing marginal posterior densities for a wide range of Bayesian problems several of which were previously inaccessible. Our purpose here is two-fold. First we flesh out the implementation of this approach for calculation of arbitrary expectations of interest. Secondly we offer comparison with perhaps the most prominent approach for calculating posterior expectations, analytic approximation involving application of the LaPlace method. Several illustrative examples are discussed as well. Clear advantages for the sampling based approach emerge.     

Minifying Government: The Unintended Consequences of the Bergman Secondary Road Act of 1929*

Objective. In 1929, Iowa adopted the Bergman Secondary Road Act, which transferred control of the state's rural roads from the townships to the counties. This study examines the interesting and potentially important unintended consequences of the law. Method. We gathered the minutes from 2,275 Iowa township meetings in 20 townships from 1917 to 1950 to investigate the effect of the Bergman Act. Results. Multiple regression analysis shows that this apparently innocuous Act turned out to have dramatic and unintended consequences on Iowa's township governments. Without responsibility for the roads, township government activity plunged dramatically—the annual number of meetings and the length of those meetings fell by half from 1929 to 1930. The effect of the law on township activity remains substantial even after controlling for competing explanations, such as the onset of the Depression. Conclusions. The Bergman Act unintentionally caused a sharp drop in township activity and it may have initiated the gradual marginalization of Iowa township governments that continues today. It is even possible that it had a depressing effect on voter turnout in rural Iowa.     

A Score Test for the Multivariate Burr and Other Weibull Mixture Distributions

The p -variate Burr distribution has been derived, developed, discussed and deployed by various authors. In this paper a score statistic for testing independence of the components, equivalent to testing for p independent Weibull against a p -variate Burr alternative, is obtained. Its null and non-null properties are investigated with and without nuisance parameters and including the possibility of censoring. Two applications to real data are described. The test is also discussed in the context of other Weibull mixture models.     

Social theory’s “constituency”

The argument is made that the relation between theory and research has become tenuous in American sociology during the recent past, and that during the earlier decades of this century the nature of that relationship was different. A suggestion is made for the reacquaintance of empirical research and its theoretical underpinning. He wroteWeber, Irrationality, and Social Order, co-editedHermeneutics, edited and published the journalHistory of Sociology for some years, is now editor ofSociological Theory, and has moved to the University of California at Riverside. Please send all correspondence to: Alan Sica, Department of Sociology, University of California-Riverside, Riverside CA 92521-0419.