A comparison of confidence intervals generated by the scheffé and bonferroni methods

Simultaneous confidence intervals for the p means of a multivariate normal random variable with known variances may be generated by the projection method of Scheffé and by the use of Bonferroni's inequality. It has been conjectured that the Bonferroni intervals are shorter than the Scheffé intervals, at least for the usual confidence levels. This conjecture is proved for all p≥2 and all confidence levels above 50%. It is shown, incidentally, that for all p≥2 Scheffé's intervals are shorter for sufficiently small confidence levels. The results are also applicable to the Bonferroni and Scheffé intervals generated for multinomial proportions.     

Tukey-Type Distributions in the Context of Financial Data

Abstract

In one-parameter (θ) families, we were not aware of explicit hypothesis testing scenarios where maximal invariant statistics failed to distinguish the models. We start with a concrete example (Sec. 2.2) to highlight such a hypothesis testing problem involving markedly different models. In this problem, because of the absence of a nontrivial uniformly most powerful invariant (UMPI) test, we briefly suggest two approaches to test the hypothesis. The first resolution (Sec. 3.1) is frequentist in nature. It utilizes a weight function on the parameter space and compares “average” distributions obtained under the null and alternative models in the sense of Wald (1947 Wald , A. ( 1947 ). Sequential Analysis . New York : Wiley . [Google Scholar] 1950 Wald , A. ( 1950 ). Statistical Decision Functions . New York : Wiley . [Google Scholar]). In contrast, a fully Bayesian resolution (Sec. 3.2) is also included. The note ends with a series of other interesting examples involving one-parameter families where maximal invariant statistics fail to distinguish the hypothesized models. The examples include easy-to-construct families of probability models involving only a single location or scale parameter θ.     

Invariant co-ordinate selection

Summary.  A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue–eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection . By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant co- ordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given.     

Sampling from spatial databases

This paper deals with techniques for obtaining random point samples from spatial databases. We seek random points from a continuous domain (usually ²) which satisfy a spatial predicate that is represented in the database as a collection of polygons. Several applications of spatial sampling (e.g. environmental monitoring, agronomy, forestry, etc) are described. Sampling problems are characterized in terms of two key parameters: coverage (selectivity), and expected stabbing number (overlap). We discuss two fundamental approaches to sampling with spatial predicates, depending on whether we sample first or evaluate the predicate first. The approaches are described in the context of both quadtrees and R-trees, detailing the sample first, acceptance/rejection tree, and partial area tree algorithms. A sequential algorithm, the one-pass spatial reservoir algorithm is also described. The relative performance of the various sampling algorithms is compared and choice of preferred algorithms is suggested. We conclude with a short discussion of possible extensions.     

Coherency conditions for finite exchangeable inference

Summary We idenify the invertible coherent functional relation between an array of asserted conditional probabilities and the probability distribution for the sum of events that are regarded exchangeably, in the regular case thatP(N _N+1 |S _N =a) ∈ (0, 1) for everya=0, 1, ...,N. The result is used to construct a useful algebraic and geometrical representation of all coherent inferences in the regular case, including those that are nonlinear in the sum of the conditioning events. The special case in which conditional probabilities mimic observed frequencies within (0, 1) receives an exact solution, which allows an easy interpretation of its surprising consequences. Finally, we introduce a new direction in research on prior opinion assessment that this approach, inverse to the usual one, suggests.     

A Method to Handle Zero Counts in the Multinomial Model

In the context of an objective Bayesian approach to the multinomial model, Dirichlet(a, …, a) priors with a < 1 have previously been shown to be inadequate in the presence of zero counts, suggesting that the uniform prior (a = 1) is the preferred candidate. In the presence of many zero counts, however, this prior may not be satisfactory either. A model selection approach is proposed, allowing for the possibility of zero parameters corresponding to zero count categories. This approach results in a posterior mixture of Dirichlet distributions and marginal mixtures of beta distributions, which seem to avoid the problems that potentially result from the various proposed Dirichlet priors, in particular in the context of extreme data with zero counts.     

Humility,Forgiveness, and Emerging Adult Female Romantic Relationships

Among a sample of emerging adult females (N = 152) we empirically examined the role of humility and forgiveness in romantic relationships. We specifically tested a model linking perceived humility to relationship satisfaction with self‐forgiveness and partner‐forgiveness. Participants in a romantic relationship completed measures of self‐reported humility, self‐forgiveness, partner‐forgiveness, and relationship satisfaction. Serial mediation analyses were conducted using path analysis to test the following sequence, humility self‐forgiveness partner‐forgiveness relationship satisfaction. Findings indicate that humility was related to relationship satisfaction via a serially mediated path of self‐forgiveness and partner‐forgiveness, which was not reducible to impression management. We consider implications for research and clinical practice.     

A Proportional Hazards Regression Model for the Subdistribution with Covariates‐adjusted Censoring Weight for Competing Risks Data

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate‐dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate‐dependent censoring. We consider a covariate‐adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate‐adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate‐adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research. Here, cancer relapse and death in complete remission are two competing risks.     

Barrios and burbs: residential context and health-risk behaviors among Angeleno adolescents

The increasing size of the Latino immigrant population in the United States underscores the need for a more complete understanding of the role that social context plays in influencing the health of immigrants and their children. This analysis explores the possibility that residential location influences the health-risk behaviors of Latino youth in Los Angeles County, California. The data come from the Los Angeles Family and Neighborhood Survey. We apply multivariate, multilevel Rasch models to two scales of adolescent health-risk behaviors (substance use and delinquency). The findings suggest that residence in Census tracts characterized by above-county-average levels of Latinos and above-county-average levels of poverty is associated with increased odds of health-risk behaviors for Latino adolescents, particularly for those born in the United States. The findings lend support to the contention, put forth in the segmented assimilation literature, that disadvantaged urban contexts increase the risk that U.S.-born children of immigrants will experience downward assimilation.     

Foreign-born emigration: A new approach and estimates based on matched CPS files

The utility of postcensal population estimates depends on the adequate measurement of four major components of demographic change: fertility, mortality, immigration, and emigration. Of the four components, emigration, especially of the foreign-born, has proved the most difficult to gauge. Without "direct" methods (i.e., methods identifying who emigrates and when), demographers have relied on indirect approaches, such as residual methods. Residual estimates, however are sensitive to inaccuracies in their constituent parts and are particularly ill-suited for measuring the emigration of recent arrivals. Here we introduce a new method for estimating foreign-born emigration that takes advantage of the sample design of the Current Population Survey (CPS): repeated interviews of persons in the same housing units over a period of 16 months. Individuals appearing in a first March Supplement to the CPS but not the next include those who died in the intervening year, those who moved within the country, and those who emigrated. We use statistical methods to estimate the proportion of emigrants among those not present in the follow-up interview. Our method produces emigration estimates that are comparable to those from residual methods in the case of longer-term residents (immigrants who arrived more than 10 years ago), but yields higher--and what appear to be more accurate--estimates for recent arrivals. Although somewhat constrained by sample size, we also generate estimates by age, sex, region of birth, and duration of residence in the United States.