寻找有理根的新方法

提出了用矩阵讨论多项式的有理根 ,用列表法一次性求出有理根 .     

(M,S)-optimal row-column designs

Row-column designs may be considered to have two blocking schemes, namely the treatments by rows and treatments by columns component block designs. The (M,S)-optimality criterion is applied to row-column designs, and che connection between the (M,S)-optimal design and its component block designs is demonstrated.     

Matrix-analytic Models and their Analysis

We survey phase-type distributions and Markovian point processes, aspects of how to use such models in applied probability calculations and how to fit them to observed data. A phase-type distribution is defined as the time to absorption in a finite continuous time Markov process with one absorbing state. This class of distributions is dense and contains many standard examples like all combinations of exponential in series/parallel. A Markovian point process is governed by a finite continuous time Markov process (typically ergodic), such that points are generated at a Poisson intensity depending on the underlying state and at transitions; a main special case is a Markov-modulated Poisson process. In both cases, the analytic formulas typically contain matrix-exponentials, and the matrix formalism carried over when the models are used in applied probability calculations as in problems in renewal theory, random walks and queueing. The statistical analysis is typically based upon the EM algorithm, viewing the whole sample path of the background Markov process as the latent variable.     

非奇异H矩阵研究

给出了非奇异Ｈ矩阵的一个必要条件和一种简单实用的判定方法     

Heteroskedasticity-consistent interval estimators

The linear regression model is commonly used in applications. One of the assumptions made is that the error variances are constant across all observations. This assumption, known as homoskedasticity, is frequently violated in practice. A commonly used strategy is to estimate the regression parameters by ordinary least squares and to compute standard errors that deliver asymptotically valid inference under both homoskedasticity and heteroskedasticity of an unknown form. Several consistent standard errors have been proposed in the literature, and evaluated in numerical experiments based on their point estimation performance and on the finite sample behaviour of associated hypothesis tests. We build upon the existing literature by constructing heteroskedasticity-consistent interval estimators and numerically evaluating their finite sample performance. Different bootstrap interval estimators are also considered. The numerical results favour the HC4 interval estimator.     

A stepwise approach for the purely periodic interaction spline model

The basic idea of an interaction spline model was presented in Barry (1983). The general interaction spline models were proposed by Wahba (1986). The purely periodic spline model, a special case of the general interaction spline models, is considered in this paper. A stepwise approach using generalized cross validation (GCV) for fitting the model is proposed. Based on the nice orthogonality properties of the purely periodic functions, the stepwise approach is a promising method for the interaction spline model. The approach can also be generalized to the non-purely-periodic spline models. But this is no done here.     

Some resolvable orthogonal arrays with two symbols

A method of constructing a resolvable orthogonal array (4λk2,2) which can be partitioned into λ orthogonal arrays (4,k 2,1) is proposed. The number of constraints kfor this type of orthogonal array is at most 3λ. When λ=2 or a multiple of 4, an orthogonal array with the maximum number of constraints of 3λ can be constructed. When λ=4n+2(n≧1) an orthogonal array with 2λ+2 constraints can be constructed. When λ is an odd number, orthogonal arrays can be constructed for λ=3,5,7, and 9 with k=4,8,12, and 13 respectively.     

The exact noncentral distribution of the generalized multiple correlation matrix

Given p×n X N(βY, ∑?I), β, ∑ unknown, the noncentral multivariate beta density of the matrix L = [(YY′)^-1/2Y X′ (XX′)^-1XY′ (YY′)^-1/2] is desired. Khatri (1964) finds this density when β is of rank unity. The present paper derives the noncentral density of L and the density of the roots matrix of L for full rank β. The dual case density of L is also obtained. The derivations are based on generalized Sverdrup's lemma, Kabe (1965), and the relationship between primal and dual density of L is explicitly established.     

Minimization of model inadequacy when observations subject to shift in means and variances

In this article optimality of experimental design for fitting a lower-order polynomial to a higher order response function for the situation in which observations may be subject to shift in means as well as in variances is considered. It is found that Karson, Manson and Hader‘s (1969) optimum designs provide pro-tection, in some sense, against model inadequacies even when observations are subject to shift in means and variances.     

Variance bounds for estimators in autoregressive models with constraints

We consider nonlinear and heteroscedastic autoregressive models whose residuals are martingale increments with conditional distributions that fulfil certain constraints. We treat two classes of constraints: residuals depending on the past through some function of the past observations only, and residuals that are invariant under some finite group of transformations. We determine the efficient influence function for estimators of the autoregressive parameter in such models, calculate variance bounds, discuss information gains, and suggest how to construct efficient estimators. Without constraints, efficient estimators can be given by weighted least squares estimators. With the constraints considered here, efficient estimators are obtained differently, as one-step improvements of some initial estimator, similarly as in autoregressive models with independent increments.