Mixed Model-Based Hazard Estimation

This article proposes a new method for estimation of the hazard function from a set of censored failure time data, with a view to extending the general approach to more complicated models. The approach is based on a mixed model representation of penalized spline hazard estimators. One payoff is the automation of the smoothing parameter choice through restricted maximum likelihood. Another is the option to use standard mixed model software for automatic hazard estimation.     

Likelihood-Based Analysis of Linear State-Space Models Using the Cholesky Decomposition

Data associated with the linear state-space model can be assembled as a matrix whose Cholesky decomposition leads directly to a likelihood evaluation. It is possible to build several matrices for which this is true. Although the chosen matrix or assemblage can be very large, rows and columns can usually be rearranged so that sparse matrix factorization is feasible and provides an alternative to the Kalman filter. Moreover, technology for calculating derivatives of the log-likelihood using backward differentiation is available, and hence it is possible to maximize the likelihood using the Newton–Raphson approach. Emphasis is given to the estimation of dispersion parameters by both maximum likelihood and restricted maximum likelihood, and an illustration is provided for an ARMA(1,1) model.     

方差分量模型协方差阵的谱分解

本文对平衡方差分量模型, 给出了其协方差阵的新的谱分解算法. 该方法的特点是计算简单, 易于理解, 无须复杂的数学知识. 且能够明确显示协方差阵的不同特征值的个数, 以及谱分解中不同特征值所对应的投影阵的显式表示. 基于新方法我们进一步研究了平衡方差分量模型的一些相关性质.本文还研究了一般方差分量模型, 我们首先定义了一般方差分量模型协方差阵的简单谱分解,给出了一般方差分量模型可以进行简单谱分解的充要条件, 并研究了协方差阵简单谱分解的一些性质. 对于协方差阵可以进行简单谱分解的方差分量模型, 本文研究了简单谱分解在其统计推断中的应用.     

计算周期三对角矩阵行列式和逆矩阵的新算法

给出了一种计算周期三对角矩阵行列式和逆矩阵的新递推算法,它们的运算复杂度分别为O(n)和O(n2),该算法是文献[5]和[6]中相关算法的拓广.     

A new method for the estimation of variance components directly from the sample covariance matrix

Statistical techniques for the estimation of variance components are usually associated with methodological and computational difficulties. In this paper a new computational method for the estimation of variance components directly from the sample covariance matrix is proposed. A comparison between this method and the maximum likelihood method for variance component estimation, based on their computational performance, is made. Cases for balanced and unbalanced simulated data assuming a two-way nixed model with correlated errors are considered, and a real-life application in animal breeding is presented.     

Instability of statistical factor analysis

Factor analysis, a popular method for interpreting multivariate data, models the covariance among variables as being due to a small number (, ) of hidden variables. A factor analysis of can be thought of as an ordered or unordered collection, , of linearly independent lines in . Let be the collection of data sets for which is defined. The ``singularities' of are those data sets, , in the closure, , at which the limit, , does not exist. is unstable near its singularities.

Let be the direct sum of the lines in . determines a -plane bundle, , over a subset, , of . If 1$"> and is rich enough, ordered or, at least if or 3, unordered, must have a singularity at some data set in . The proofs are applications of algebraic topology. Examples are provided.

     

Twisted factorization of a banded matrix

The twisted factorization of a tridiagonal matrix T plays an important role in inverse iteration as featured in the MRRR algorithm. The twisted structure simplifies the computation of the eigenvector approximation and can also improve the accuracy. A tridiagonal twisted factorization is given by T=M _k Δ _k N _k where Δ _k is diagonal, M _k ,N _k have unit diagonals, and the k-th column of M _k and the k-th row of N _k correspond to the k-th column and row of the identity, that is . This paper gives a constructive proof for the existence of the twisted factorizations of a general banded matrix A. We show that for a given twist index k, there actually are two such factorizations. We also investigate the implications on inverse iteration and discuss the role of pivoting.      

An extension of the Fiedler-Markham determinant inequality

We extend a determinant inequality of Fiedler and Markham [On a theorem of Everitt, Thompson, and de Pillis, Math Slovaca, 44 (1994), 441–444] to the class of matrices whose numerical range is contained in a sector. Moreover, some related results are also included.     

A New,Fast Algorithm to Find the Regions of Possible Support for Bivariate Interval-Censored Data

The estimation of the nonparametric maximum likelihood estimate (NPMLE) of the bivariate distribution function on interval-censored data is a recent topic of research. Among other things, it provides a basic tool for checking a parametric model for the bivariate failure times. As a first step in the estimation of the NPMLE for bivariate interval-censored data, the regions of possible support—that is, the rectangles with nonzero mass—are calculated. For this step a new, fast algorithm is introduced here and compared with two existing algorithms. The advantages of our algorithm will be illustrated on the emergence times of permanent teeth on data from the longitudinal Signal® Tandmobiel study.     

实四元数矩阵行列式函数的几点注记

分别对实四元数矩阵理论中出现的几种行列式函数在三个初等变换下的改变性作一些讨论,得出几种满足一定性质的行列式函数的不存在性或唯一存在性。     

Pareto分布环境因子的估计及其应用

给出了Pareto分布环境因子的定义,讨论了在定数截尾样本下Pareto分布环境因子的极大似然估计和修正极大似然估计,并尝试把环境因子用于可靠性评估中.最后运用Monte Carlo方法对极大似然估计,修正极大似然估计和可靠性指标的均方误差(MSE),进行了模拟比较,结果表明修正极大似然估计优于极大似然估计且考虑环境因子的可靠性评估结果较好.     

Mathematical proof of closed form expressions for finite difference approximations based on Taylor series

Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were based on observation of numerical results. In this paper, we provide a mathematical proof of those formulas by deriving them mathematically from the Taylor series.     

Exact maximum likelihood estimator of the structure of a stratified population

An exact expression for the extreme values of the integer vector that maximize the function

全非负阵的Hadamard—Fischer不等式的几个改进

本文讨论了全非负阵与其逆矩阵的关系，改进了关于全非负矩阵的Hadamard－Fischer不等式的几个近期结果．     

On the Cholesky factorization of the Gram matrix of locally supported functions

Cholesky factorization of bi-infinite and semi-infinite matrices is studied and in particular the following is proved. If a bi-infinite matrixA has a Cholesky factorization whose lower triangular factorL and its lower triangular inverse decay exponentially away from the diagonal, then the semi-infinite truncation ofA has a lower triangular Cholesky factor whose elements approach those ofL exponentially. This result is then applied to studying the asymptotic behavior of splines obtained by orthogonalizing a large finite set of B-splines, in particular identifying the limiting profile when the knots are equally spaced.The first and second authors were partially supported by Nato Grant #920209, the second author also by the Alexander von Humboldt Foundation, and the last two authors by the Italian Ministry of University and Scientific and Technological Research.