Models and methods for pairing data

This paper deals with models and methods for count data derived from observations on pairing phenomena. Pairs formed from “similar” members are excluded. Various models are considered and analyzed. Particular emphasis is on developing methods for testing whether particular pairs are prone to occur more or less often than expected by chance.     

Approximate optimal allocation in repeated sampling from a finite population

Samples of size n are drawn from a finite population on each of two occasions. On the first occasion a variate x is measured, and on the second a variate y. In estimating the population mean of y, the variance of the best linear unbiased combination of means for matched and unmatched samples is itself minimized, with respect to the sampling design on the second occasion, by a certain degree of matching. This optimal allocation depends on the population correlation coefficient, which previous authors have assumed known. We estimate the correlation from an initial matched sample, then an approximately optimal allocation is completed and an estimator formed which, under a bivariate normal superpopulation model, has model expected mean square error equal, apart from an error of order n^-2, to the minimum enjoyed by any linear, unbiased estimator.     

On a multiple endpoints testing problem

In a clinical trial comparing drug with placebo, where there are multiple primary endpoints, we consider testing problems where an efficacious drug effect can be claimed only if statistical significance is demonstrated at the nominal level for all endpoints. Under the assumption that the data are multivariate normal, the multiple endpoint-testing problem is formulated. The usual testing procedure involves testing each endpoint separately at the same significance level using two-sample t-tests, and claiming drug efficacy only if each t-statistic is significant. In this paper we investigate properties of this procedure. We show that it is identical to both an intersection union test and the likelihood ratio test. A simple expression for the p-value is given. The level and power function are studied; it is shown that the test may be conservative and that it is biased. Computable bounds for the power function are established.     

A study of BIB designs through support matrices

This paper deals with the existence and nonexistence of BIB designs with repeated blocks. The approach is an algebraic one. The concept of a support matrix is introduced and some of its basic properties are noted. Some basic examples of support matrices are given when the block size is 3. The connection between full column rank proper support matrices and irreducible designs is explored and some examples of such matrices are given.     

Some new factor screening designs using the search linear model

Factor screening designs for searching two and three effective factors using the search linear model are discussed. The construction of such factor screening designs involved finding a fraction with small number of treatments of a 2^m factorial experiment having the property P_2t (no 2t columns are linearly dependent) for t=2 and 3. A ‘Packing Problem’ is introduced in this connection. A complete solution of the problem in one case and partial solutions for the other cases are presented. Many practically useful new designs are listed.     

Goodness-of-fit tests for a heavy tailed distribution

We study the Kolmogorov–Smirnov test, Berk–Jones test, score test and their integrated versions in the context of testing the goodness-of-fit of a heavy tailed distribution function. A comparison of these tests is conducted via Bahadur efficiency and simulations.     

Estimating conditional tail expectation with actuarial applications in view

We develop statistical inferential tools for estimating and comparing conditional tail expectation (CTE) functions, which are of considerable interest in actuarial science. In particular, we construct estimators for the CTE functions, develop the necessary asymptotic theory for the estimators, and then use the theory for constructing confidence intervals and bands for the functions. Both parametric and non-parametric approaches are explored. Simulation studies illustrate the performance of estimators in various situations. Results are obtained under minimal assumptions, and the general Vervaat process plays a crucial role in achieving these goals.     

On Christensen's conjecture

In this paper we give solution to a conjecture appearing in Christensen (1997, p. 360) in relation to the definitions of standardized residuals in loglinear models. Work done when he was visiting as the Distinguished Lukacs Professor on leave from the Complutense University of Madrid. An erratum to this article is available at .     

Minimum contrast estimation of random processes based on information of second and third orders

This paper presents the results on consistency and asymptotic normality of a class of minimum contrast estimators for random processes with short- or long-range dependence based on the second- and third-order cumulant spectra. Asymptotic properties of sample spectral functionals of second and third orders, which are of independent interest in view of their possible use for nonparametric estimation of processes with short- or long-range dependence, are also provided.     

A multivariate version of Gini's rank association coefficient

In this paper, we introduce a multivariate generalization of the population version of Gini's rank association coefficient, giving a response to this open question posed in [4]. We also study some properties of this version, present the corresponding results for the sample statistic, and provide several examples.