线性空间的幂等变换与对合变换的几个等价表示

给出数域F上线性空间(不一定是有限维的)的线性变换是对合变换与幂等变换的几个等价描述.作为其推论,得到数域F上n阶方阵是对合矩阵与幂等矩阵的几个等价描述.     

Double hierarchical generalized linear models (with discussion)

Summary.  We propose a class of double hierarchical generalized linear models in which random effects can be specified for both the mean and dispersion. Heteroscedasticity between clusters can be modelled by introducing random effects in the dispersion model, as is heterogeneity between clusters in the mean model. This class will, among other things, enable models with heavy-tailed distributions to be explored, providing robust estimation against outliers. The h -likelihood provides a unified framework for this new class of models and gives a single algorithm for fitting all members of the class. This algorithm does not require quadrature or prior probabilities.     

Design and analysis of computer experiments when the output is highly correlated over the input space

To build a predictor, the output of a deterministic computer model or “code” is often treated as a realization of a stochastic process indexed by the code's input variables. The authors consider an asymptotic form of the Gaussian correlation function for the stochastic process where the correlation tends to unity. They show that the limiting best linear unbiased predictor involves Lagrange interpolating polynomials; linear model terms are implicitly included. The authors then develop optimal designs based on minimizing the limiting integrated mean squared error of prediction. They show through several examples that these designs lead to good prediction accuracy.     

Multilevel Models in Family Research: Some Conceptual and Methodological Issues

Examining the impact of context on individual‐level outcomes has become an increasingly common undertaking in the social sciences. The growth in concern for identifying the effects of macrolevel characteristics has generated both theoretical and methodological advancements. In this issue of Journal of Marriage and Family, Butler (2002) researches whether the effect of welfare benefit levels on premarital childbearing varies by context, Hoffmann (2002) researches the effect of context on adolescent drug use, and Simons et al. (2002) examine how the relationship between parenting and child conduct varies by context. These articles are used as a background to discuss important theoretical and methodological issues surrounding the analysis of multilevel data. The authors present a simple analysis of data pertaining to age at first marriage taken from the Panel Study of Income Dynamics and merged with census data to measure contextual effects as a pedagogical device for introducing readers to the benefits of multilevel modeling.     

Linear functional regression: The case of fixed design and functional response

The authors consider the problem of simple linear regression when the exogenous and endogenous variables are functional and the design is fixed. They propose an estimator for the underlying linear operator and prove its consistency under some conditions which ensure that the design is sufficiently informative. They consider the classical calibration (or inverse regression) problem and analyze a consistent estimator. They also give a simulation study. The proposed method is not hard to implement in practice.     

信号方向误差对自适应阵的影响

讨论信号方向偏离约束方向(即信号方向误差)对线性约束自适应阵性能的影响.把输出信噪比看作是信号方向和输入信噪比的函数,研究了输出信噪比同信号方向和输入信噪比的关系.通过分析,结果发现在一定的输入信噪比下,要求的输出信噪比越大,信号方向误差就应越小;对具有一定方向误差的信号,输入信噪比越大,有用信号受到的抑制就越厉害;当干扰信号存在时,阵对信号方向误差的敏感度减少.     

Iterative weighted least-squares estimates in a heteroscedastic linear regression model

The aim of this study is to improve the efficiency of weighted least-squares estimates for a regression parameter. An iterative procedure, starting with an unbiased estimate other than the unweighted least-squares estimate, yields estimates which are asymptotically more efficient than the feasible generalized least-squares estimate when errors are spherically distributed. The result has an application in the improvement of the Graybill–Deal estimate of the common mean of several normal populations.     

Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections

Summary. The paper presents a reinterpretation of the model underpinning the Lee–Carter methodology for forecasting mortality (and other vital) rates. A parallel methodology based on generalized linear modelling is introduced. The use of residual plots is proposed for both methods to aid the assessment of the goodness of fit. The two methods are compared in terms of structure and assumptions. They are then compared through an analysis of the gender- and age-specific mortality rates for England and Wales over the period 1950–1998 and through a consideration of the forecasts generated by the two methods. The paper also compares different approaches to the forecasting of life expectancy and considers the effectiveness of the Coale–Guo method for extrapolating mortality rates to the oldest ages.     

《线性代数》课程教学改革的实践与思考

从线性代数课程的教学现状、内容结构,现行教材的体系为出发点,在课程体系、教学内容等方面提出了在注重经典理论内容的同时,应渗透现在教学的观念、思想和方法.在教学方法和教学手段方面阐明了运用启发式教学方法以及穿透教学手段和多媒体教学手段相结合的意义和作用,提出了一些教学改革的建议.     

隐非齐次马尔可夫多元线性回归模型及其贝叶斯估计

隐马尔可夫模型对于异质纵向数据的处理有良好的效果,因此被广泛应用于工程技术、生物医学、经济管理等领域。文章引入了一种特殊的非齐次隐马尔可夫状态转移方式,并将其与经典的多元线性回归相结合,提出了隐非齐次马尔可夫多元线性回归模型,介绍了对该模型进行贝叶斯推断的方法原理和技术细节。最后,通过两个模拟实验说明了推断方法的结果是可靠的。