A note on connectedness in fixed effects manova and gmanova models withmissing cells

Murray and Smith (1985) and Hocking (1985) give a generalized definition and test of connectedness in the case of missing cells using the univariate cell-means model with linear restrictions on the cell-means. The test of connectedness is here extended to multivariate fixed effects models, including the usual MANOVA model with linear restrictions, the MANOVA model with double linear restrictions, and the GMANOVA model.     

D-optimal design for a quadratic log contrast model for experiments with mixtures

A practical method is suggested for solving complicated D-optimal design problems analytically. Using this method the author has solved the problem for a quadratic log contrast model for experiments with mixtures introduced by J. Aitchison and J. Bacon-Shone. It is found that for a symmetric subspace of the finite dimensional simplex, the vertices and the centroid of this subspace are the only possible support points for a D-optimal design. The weights that must be assigned to these support points contain irrational numbers and are constrained by a system of three simultaneous linear equations, except for the special cases of 1- and 2-dimensional simplexes where the situation is much simpler. Numerical values for the solution are given up to the 19-dimensional simplex     

Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths

We obtain the rates of pointwise and uniform convergence of multivariate kernel density estimators using a random bandwidth vector obtained by some data-based algorithm. We are able to obtain faster rate for pointwise convergence. The uniform convergence rate is obtained under some moment condition on the marginal distribution. The rates are obtained under i.i.d. and strongly mixing type dependence assumptions.     

Applications of quadrivariate exponential distribution to a three-unit warm standby system with dependent structure

Two-unit warm standby systems have been elaborately dealt within the literature. However, the study of standby systems with more than two units, though very relevant in state-of-the-art practical situations, has received little attention because of mathematical intricacies involved in analyzing them. Also, such systems have been studied assuming: (i) the lifetime or repair time of the units to be exponential, or (ii) the lifetime and repair time to be independent. The present contribution is an improvement in the state-of-the-art in the sense that three-unit warm standby system with dependent structure is shown to be capable of comprehensive analysis.     

Information matrix for a mixture of two inverse gaussian distributions

In this paper, Fisher information matrix about the five parameters ρ, μ_:1, μ², λ¹and λ²of a mixture of two Inverse Gaussian density functions is obtained. The Leguerre-Gauss quadrature formula is used to evaluate the essential integral on which the twenty five elements of the information matrix are based. Results involving the computation of the information about p are compared with those involving both the power series expansion and Simpson's method of integration. Laguerre-Gauss quadra-ture was found to lead to good approximations as compared with other methods. It was therefore chosen for the computations of the elements of the information matrix.     

Approximations to the multivariate normal integral

We propose a simple and efficient way to approximate multivariate normal probabilities using univariate and bivariate probabilities. The approximation is computationally tested for the trivariate and quadrivariate normal probabilities. A few problems of higher dimensions were also tested.     

Updating discriminant functions estimated from inverse gaussian populations

The problem of updating discriminant functions estimated from inverse Gaussian populations is investigated in situations when the additional observations are mixed (unclassified) or classified. In each case two types of discriminant functions, linear and quadratic, are considered. Using simulation experiments the performance of the updating procedures is evaluated by means of relative efficiencies.     

Bayesian classification with multivariate autoregressive sources that might have different orders

The main objective of this paper is to develop an exact Bayesian technique that can be used to assign a multivariate time series realization to one of several autoregressive sources, with unknown coefficients and precision, that might have different orders. The foundation of the proposed technique is to develop the posterior mass function of a classification vector, in an easy form, using the conditional likelihood function. A multivariate time series realization is assigned to the multivariate autoregressive source with the largest posterior probability. A simulation study, with uniform prior mass function, is carried out to demonstrate the performance of the proposed technique and to test its adequacy in handling the multivariate classification problems. The analysis of the numerical results supports the adequacy of the proposed technique in solving the classification problems with multivariate autoregressive sources.     

A class of semiparametric transormation frailty models with application to estimating treatment effects and heterogenity in aids clinical traials

Muitivariate failure time data are common in medical research; com¬monly used statistical models for such correlated failure-time data include frailty and marginal models. Both types of models most often assume pro¬portional hazards (Cox, 1972); but the Cox model may not fit the data well This article presents a class of linear transformation frailty models that in¬cludes, as a special case, the proportional hazards model with frailty. We then propose approximate procedures to derive the best linear unbiased es¬timates and predictors of the regression parameters and frailties. We apply the proposed methods to analyze results of a clinical trial of different dose levels of didansine (ddl) among HIV-infected patients who were intolerant of zidovudine (ZDV). These methods yield estimates of treatment effects and of frailties corresponding to patient groups defined by clinical history prior to entry into the trial.     

The estimation of treatment effect for the censored bivariate data under the univariate censoring

This paper establishes a nonparametric estimator for the treatment effect on censored bivariate data under unvariate censoring. This proposed estimator is based on the one from Lin and Ying(1993)'s nonparametric bivariate survival function estimator, which is itself a generalized version of Park and Park(1995)' quantile estimator. A Bahadur type representation of quantile functions were obtained from the marginal survival distribution estimator of Lin and Ying' model. The asymptotic property of this estimator is shown below and the simulation studies are also given