A generalized scheffé method of multiple comparisons

Standard resulrs on the extrema of quotients of quadratic forms are extended to the non-negative definite case. The maximum and the set over which it is achieved are characterized explicitly both in terms of generalized inverse matrices and generalized eigenvalues. These results become the basis of Scheffe type multiple comparisons in the usual way. To demonstrate their application to statistics with singular covariance matrices, the method is detailed for Mantel-Haenszel, Breslow, and Cox statistics. An example is presented illustrating a situation where the proposed Scheffe type comparisons may be better than the pairwise method.     

Multiple Time Series Modeling and Extended Sample Cross-Correlations

This article provides an expository account of the multivariate autoregressive moving average models and proposes an extended sample cross-correlation approach for practical model identification. An iterative model building procedure for applying these models to real data is discussed and demonstrated by analyzing the 5-series U.S. Hog Data.     

COMPARATIVE CALIBRATION WITH SUBGROUPS

The main object of this paper is to consider structural comparative calibration models under the assumption that the unknown quantity being measured is not identically distributed for all units. We consider the situation where the mean of the unknown quantity being measured is different within subgroups of the population. Method of moments and maximum likelihood estimators are considered for estimating the parameters in the model. Large sample inference is facilitated by the derivation of the asymptotic variances. An application to a data set which indeed motivated the consideration of such general model and was obtained by measuring the heights of a group of trees with five different instruments is considered.     

On the use of partial confounding for the construction of alternative regular two-level blocked fractional factorial designs

In this paper, we consider experimental situations in which a regular fractional factorial design is to be used to study the effects of m two-level factors using n=2^m−k experimental units arranged in 2^p blocks of size 2^m−k−p. In such situations, two-factor interactions are often confounded with blocks and complete information is lost on these two-factor interactions. Here we consider the use of the foldover technique in conjunction with combining designs having different blocking schemes to produce alternative partially confounded blocked fractional factorial designs that have more estimable two-factor interactions or a higher estimation capacity or both than their traditional counterparts.     

Generalized Weibull Linear Models

For the first time, a new class of generalized Weibull linear models is introduced to be competitive to the well-known generalized (gamma and inverse Gaussian) linear models which are adequate for the analysis of positive continuous data. The proposed models have a constant coefficient of variation for all observations similar to the gamma models and may be suitable for a wide range of practical applications in various fields such as biology, medicine, engineering, and economics, among others. We derive a joint iterative algorithm for estimating the mean and dispersion parameters. We obtain closed form expressions in matrix notation for the second-order biases of the maximum likelihood estimates of the model parameters and define bias corrected estimates. The corrected estimates are easily obtained as vectors of regression coefficients in suitable weighted linear regressions. The practical use of the new class of models is illustrated in one application to a lung cancer data set.     

Schur optimality of one-way designs

In comparison of treatments using homogeneous experimental units, it is shown that a design is Schur optimal when treatment replications are as equal as possible.     

Central Limit Theorem approximations for the number of runs in Markov-dependent binary sequences

We consider Markov-dependent binary sequences and study various types of success runs (overlapping, non-overlapping, exact, etc.) by examining additive functionals based on state visits and transitions in an appropriate Markov chain. We establish a multivariate Central Limit Theorem for the number of these types of runs and obtain its covariance matrix by means of the recurrent potential matrix of the Markov chain. Explicit expressions for the covariance matrix are given in the Bernoulli and a simple Markov-dependent case by expressing the recurrent potential matrix in terms of the stationary distribution and the mean transition times in the chain. We also obtain a multivariate Central Limit Theorem for the joint number of non-overlapping runs of various sizes and give its covariance matrix in explicit form for Markov dependent trials.     

New difference-based estimator of parameters in semiparametric regression models

The paper introduces a new difference-based Liu estimator β?_Ldiff=([Xtilde]′[Xtilde]+I)^?1([Xtilde]′[ytilde]+η β?_diff) of the regression parameters β in the semiparametric regression model, y=Xβ+f+?. Difference-based estimator, β?_diff=([Xtilde]′[Xtilde])^?1[Xtilde]′[ytilde] and difference-based Liu estimator are analysed and compared with respect to mean-squared error (mse) criterion. Finally, the performance of the new estimator is evaluated for a real data set. Monte Carlo simulation is given to show the improvement in the scalar mse of the estimator.     

On Comparison Of Estimates Of Dispersion Using Generalized Pitman Nearness Criterion

In this paper, estimates QP dispersion matrix and its functions are compared based on generalized Pitman nearness criterion, Various Iosa functions are considered for the purpose. Locally superior estimates are defined and obtained. Comparison of these estimates are made with other standard ones. It is snown that within certain classes, defined in the paper, these are the best estimatcrs ia the generalized Fitman nearness sense     

基于区间数大小不能直接判定的灰矩阵博弈的策略优超及其最优解研究

对于区间灰数大小不能直接判定的灰矩阵博弈G(⊗)={S₁,S₂,A(⊗)}问题,其策略优超和纯策略求解问题的关键在于A(⊗)中区间灰数大小判定准则的设定与判定方法的设计。本文运用灰色系统思想和系统工程的理论,揭示了人们在灰信息条件下的博弈心理与博弈决策规则,根据区间灰数势关系的判定规则,提出了灰数势意义下的策略优超法则,定义了纯策略解。最后,以商业银行贷款动态损失准备金计提为案例,对其灰势意义下的策略优超和纯策略解问题进行了研究。