Ranges of Measures of Association for Familial Binary Variables

Familial binary data occur in a wide range of scientific investigations. Numerous measures of association have been proposed in the literature for the study of intra-family dependence of the binary variables. These measures include correlations, odd ratios, kappa statistics, and relative risks. We study the permissible ranges of these measures of association such that a joint distribution exists for the familial binary variables. Our results are useful for developing efficient estimation methods for the measures of association.     

Moment Information for Probability Distributions,Without Solving the Moment Problem. I: Where is the Mode?

How much information does a small number of moments carry about the unknown distribution function? Is it possible to explicitly obtain from these moments some useful information, e.g., about the support, the modality, the general shape, or the tails of a distribution, without going into a detailed numerical solution of the moment problem? In this paper a theoretical result of Johnson and Rogers is generalized to be valid for all moment problems and is exploited to demonstrate that a few moments are able to provide us with valuable information about the position of the mode of an unknown (unimodal) distribution.     

Simultaneous Confidence Intervals for the Parameters of Pareto Distribution under Progressive Censoring

In this article, we consider the progressive Type II right censored sample from Pareto distribution. We introduce a new approach for constructing the simultaneous confidence interval of the unknown parameters of this distribution under progressive censoring. A Monte Carlo study is also presented for illustration. It is shown that this confidence region has a smaller area than that introduced by Ku? and Kaya (2007 Ku? , C. , Kaya , M. F. ( 2007 ). Estimation for the parameters of the Pareto distribution under progressive censoring . Commun. Statist. Theor. Meth. 36 : 1359 – 1365 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).     

Unbiasedness of two-stage estimation and prediction procedures for mixed linear models

The traditional method for estimating or predicting linear combinations of the fixed effects and realized values of the random effects in mixed linear models is first to estimate the variance components and then to proceed as if the estimated values of the variance components were the true values. This two-stage procedure gives unbiased estimators or predictors of the linear combinations provided the data vector is symmetrically distributed about its expected value and provided the variance component estimators are translation-invariant and are even functions of the data vector. The standard procedures for estimating the variance components yield even, translation-invariant estimators.     

On the recovery of intra- and interblock information in n-ary designs

This note presents an extension of Q-method of analysis for binary designs given by Rao (1956) to n-ary balanced and partially balanced block designs. Here a linked n-ary block (LNB) design is defined as the dual of balanced n-ary (BN) design. Having a note on Yates’ (1939, 1940) method of P-analysis, we further extend the expressions for binary linked block (LB) designs given by Rao (1956) to linked n-ary block (LNB) designs which admit easy estimation of parameters for these type of all n-ary designs.     

Use of balanced bipartite weighing designs as chemical balance designs

This paper deals with the use of balanced bipartite weighing designs as chemical balance designs when there Is a restriction on the number of objects that can be placed on either pan..The variance of each estimated weight and the covarlance of each pair of estimated weights are worked out.The use of additional weighing when the design matrix is singular is discussed.     

Age-period-cohort analysis: an illustration of the problems in assessing interaction in one observation per cell data

This paper discusses the specific problems of age-period-cohort (A-P-C) analysis within the general framework of interaction assessment for two-way cross-classified data with one observation per cell. The A-P-C multiple classification model containing the effects of age groups (rows), periods of observation (columns), and birth cohorts (diagonals of the two-way table) is characterized as one of a special class of models involving interaction terms assumed to have very specific forms. The so-called A-P-C identification problem, which results from the use of a particular interaction structure for detecting cohort effects, is shown to manifest itself in the form of an exact linear dependency among the columns of the design matrix. The precise relationship holding among these columns is derived, as is an explicit formula for the bias in the parameter estimates resulting from an incorrect specification of an assumed restriction on the parameters required to solve the normal equations. Current methods for modeling A-P-C data are critically reviewed, an illustrative numerical example is presented, and one potentially promising analysis strategy is discussed. However, gien the large number of possible sources for error in A-P-C analyses, it is strongly recommended that the results of such analyses be interpreted with a great deal of caution.     

Asymptotic non-null distribution of a test of equality of exponential populations

In this paper further asymptotic expansions of the non-null distribution of the likelihood ratio criterion for testing the equality of several one parameter exponential distributions are obtained when the alternatives are close to the hypothesis. These expansions are obtained for the first time in terms of beta distributions.