Scale estimators for symmetric stable distributions

This paper reports on a simulation comparison of scale estimators for symmetric stable distributions in terms of their ability to identify the population with the greater scale. The modified geometric mean is found to be superior to the sample standard deviation and the Fama-Roll estimator for the larger values of the characteristic exponent, while the Fama-Roll estimator is judged superior for the smaller values. Further, this study sheds some light on the question of the appropriate sample size for discriminating risk measurement in investment analysis when the samples are taken from symmetric stable distributions.     

Smoothed Mann–Whitney–Wilcoxon Procedure for Two-Sample Location Problem

This study is mainly concerned with estimating a shift parameter in the two-sample location problem. The proposed Smoothed Mann–Whitney–Wilcoxon method smooths the empirical distribution functions of each sample by using convolution technique, and it replaces unknown distribution functions F(x) and G(x ? Δ₀) with the new smoothed distribution functions F _s (x) and G _s (x ? Δ₀), respectively. The unknown shift parameter Δ₀ is estimated by solving the gradient function S _n (Δ) with respect to an arbitrary variable Δ. The asymptotic properties of the new estimator are established under some conditions that are similar to the Generalized Wilcoxon procedure proposed by Anderson and Hettmansperger (1996 Anderson , G. F. , Hettmansperger , T. P. ( 1996 ). Generalized Wilcoxon methods for the one and two-sample location models . In: Brunner , E. , Denker , M. , eds. Research Developments in Probability and Statistics: Festschrift in Honor of Madan L. Puri on the Occasion of his 65th Birthday . Zeist, The Netherlands : VSP BV , pp. 303 – 317 . [Google Scholar]). Some of these properties are asymptotic normality, asymptotic level confidence interval, and hypothesis testing for Δ₀. Asymptotic relative efficiency of the proposed method with respect to the least squares, Generalized Wilcoxon and Hodges and Lehmann (1963 Hodges , J. L. , Lehmann , E. L. ( 1963 ). Estimates of location based on rank tests . Ann. Mathemat. Statist. 34 : 598 – 611 .[Crossref] , [Google Scholar]) procedures are also calculated under the contaminated normal model.     

A Computer Program for Evaluating and Comparing Experimental Designs and Some Applications

For the past decade low cost computer graphics terminals have consisted almost exclusively of direct view storage tube (DVST) devices. Recently, however, a new variety of terminal based on “raster TV technology” has emerged which is competitive with storage tubes in price and readily supports variable intensity and color.

We summarize the basic organization of raster terminals so as to indicate their capabilities, discuss their advantages and disadvantages, and illustrate some of their uses in statistics and elsewhere. Because color is almost universally available on these terminals, we also discuss some elementary principles of color perception and use. An understanding of this material will help the data analyst present data effectively.     

Ethnic differences in symptom presentation of sexually abused girls

Although researchers have begun to examine the issue of ethnic and cultural factors in childhood sexual abuse (CSA), relatively little has been done to look at possible ethnic and cultural differences in psychological symptoms related to CSA. This study investigated the relationship between ethnicity and symptom presentation among Hispanic, African American, and Caucasian sexually abused girls. The study examined the relationship between ethnicity and depression, ethnicity and post-trauma intrusive symptoms, and ethnicity and post-trauma avoidance symptoms. Results indicated that African American girls had significantly higher levels of post-trauma avoidance symptoms than Hispanic girls, but not Caucasian girls. No significant differences were found between ethnic groups for depression or intrusive symptoms.