On the analysis of multivariate repeated measures designs

The relationship between the mixed-model analysis and multivariate approach to a repeated measures design with multiple responses is presented. It is shown that by taking the trace of the appropriate submatrix of the hypothesis (error) sums of squares and crossproducts (SSCP) matrix obtained from the multivariate approach, one can get the hypothesis (error) SSCP matrix for the mixed-model analysis. Thus, when analyzing data from a multivariate repeated measures design, it is advantageous to use the multivariate approach because the result of the mixed-model analysis can also be obtained without additional computation.     

Multiplicative Adjustment Method for Semiparametric Regression with Mixing Dependent Data

In this article, we extend a semiparametric regression estimator with multiplicative adjustment to time series context. The asymptotic theory and results from a simulation study are discussed. Theoretical results and numerical comparison show that, in the time series case, the semiparametric estimator is better than the traditional local polynomial estimator in a wide neighbourhood around the true regression function.     

A prior-valued estimator applied to multinomial classification

A multinomial classification rule is proposed based on a prior-valued smoothing for the state probabilities. Asymptotically, the proposed rule has an error rate that converges uniformly and strongly to that of the Bayes rule. For a fixed sample size the prior-valued smoothing is effective in obtaining reason¬able classifications to the situations such as missing data. Empirically, the proposed rule is compared favorably with other commonly used multinomial classification rules via Monte Carlo sampling experiments     

Dependence function for continuous bivariate densities

The notion of cross-product ratio for discrete two-way contingency table is extended to the case of continuous bivariate densities. This results in the “local dependence function” that measues the margin-free dependence between bivariate random variables. Properties and examples of the dependence function are discussed. The bivariate normal density plays a special role since it has constant dependence. Continuous bivariate densities can be constructed by specifying the dependence function along with two marginals in analogy to the construction of two-way contingency tables given marginals and patterns of interaction. The dependence function provides a partial ordering on bivariate dependence.     

Performance analysis of the retrial queues with finite number of sources and service interruptions

This paper aims at presenting an analytic approach for investigating a single-server retrial queue with finite population of customers where the server is subject to interruptions. A free source may generate a primary call to request service. If the server is free upon arrival, the call starts to be served and the service times are independent, generally distributed random variables. During the service time the source cannot generate a new primary call. After service the source moves into the free state and can generate a new primary call. There is no waiting space in front of the server, and a call who finds the server unavailable upon arrival joins an orbit of unsatisfied customers. The server is subject to interruptions during the service processes. When the server is interrupted, the call being served just before server interruption goes to the retrial orbit and will retry its luck after a random amount of time until it finds the server available. The recovery times of the interrupted server are assumed to be generally distributed. Our analysis extends previous work on this topic and includes the analysis of the arriving customer’s distribution, the busy period, and the waiting time process.     

On the estimation of variance components in stability analysis

Chow and Shao (1989, 1991) indicated that the presence of batch-to-batch variation has an impact on the determination of drug shelf-life in stability studies. In this paper, we propose two unbiased estmators for batch-to-batch variation. The proposed estimators are compared in terms of their corresponding variances. An example concerning a stability study is discussed to illustrate the use of the proposed estimators.     

Marginally oversaturated designs

A special class of supersaturated design, called marginally over saturated design (MOSD), in which the number of variables under investigation (k) is only slightly larger than the number of experimental runs (n), is presented. Several optimality criteria for supersaturated designs are discussed. It is shown that the resolution rank criterion is most appropriate for screening situations. The construction method builds on two major theorems which provide an efficient way to evaluate resolution rank. Examples are given for the cases n=8, 12, 16, and 20. Potential extensions for future work are discussed.     

An alternative proof for a version of cochran's theorem under elliptical settings

For an elliptically contoured n × p random matrix Y with mean μ and covariance proportional to ∑_Y, the necessary and sufficient conditions, under which (Y?μ)′W(Y?μ) with nonnegative definite W is generalized Wishart distributed, are obtained by using the higher moments of Y. This version of Cochran's theorem is general as the assumptions on ∑_Y=A?∑ with nonnegative definite A and ∑, P(Y?μ)=0, and P(Y≠μ)<1 have been relaxed. An example on two way balanced mixed models is given for illustration ot our main results.     

Phase-shifting common cycles and common trends

In this paper, we outline a framework for modelling and analysing economic fluctuations and dynamics. It is assumed that there may exist common trends and common cycles in the time series to be analysed It is further generalised that common cycles may have non-coincident, or phase-shifting attributes These attributes are examined via the Markov transition matrix in a VAR system, revealing the way in which the phase-shifting works with the reduced rank Markov transition matrix. The links with the structural common trend model are also presented.