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Summary. Searching for an effective dimension reduction space is an important problem in regression, especially for high dimensional data. We propose an adaptive approach based on semiparametric models, which we call the (conditional) minimum average variance estimation (MAVE) method, within quite a general setting. The MAVE method has the following advantages. Most existing methods must undersmooth the nonparametric link function estimator to achieve a faster rate of consistency for the estimator of the parameters (than for that of the nonparametric function). In contrast, a faster consistency rate can be achieved by the MAVE method even without undersmoothing the nonparametric link function estimator. The MAVE method is applicable to a wide range of models, with fewer restrictions on the distribution of the covariates, to the extent that even time series can be included. Because of the faster rate of consistency for the parameter estimators, it is possible for us to estimate the dimension of the space consistently. The relationship of the MAVE method with other methods is also investigated. In particular, a simple outer product gradient estimator is proposed as an initial estimator. In addition to theoretical results, we demonstrate the efficacy of the MAVE method for high dimensional data sets through simulation. Two real data sets are analysed by using the MAVE approach.     

随机系统计算机模拟及定理条件的讨论

讨论随机服务系统的计算机模拟,对任意输入过程的随机服务系统均可由许算机产生其全部工作情况,为对系统进行各种研究创造了条件。最后讨论了文中主要定理的条件。     

接地旋转四次圆纹导体曲面的静电问题

提出接地旋转四次圆纹导体曲面的静电问题,并在反演扁旋转椭球坐标系下进行求解。给出均匀场中接地旋转四次圆纹导体曲面的外域电位分布解析表达式。     

旋转目标R-D成像处理方法的一些基本特性

本文针对旋转目标 ISAS 成像中的距离—多普勒(R-D)处理方法,讨论了它的来源和应用条件,并着重分析了它对目标中部和边缘部分不同的分辨处理能力。本文讨论的目标在于更深刻地认识 R-D 成像处理方法,以便准确地应用它。     

Dimension reduction for the conditional kth moment in regression

The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction. Here, we introduce the central k th-moment subspace to capture information from the mean, variance and so on up to the k th conditional moment of the regression. New methods are studied for estimating these subspaces. Connections with sliced inverse regression are established, and examples illustrating the theory are presented.     

解一維电磁逆散射問題的两种数值方法

本文对两种不同的介质层模型的逆散射问题进行数值求解。第一种是对端接纯导体板的一维离散非均匀介质层求逆,采用的是变尺度参量优化方法,所得到的性能指数数值结果为10~(-7)。第二种是对一维连续非均匀介质层求逆,本文提出是将松弛法引入迭代蛙跃法中,使迭代加速,从而减少迭代次数。计算了几个例子,结果表明,松弛法的引入可使迭代次数减少,在典型例中,迭代次数可减少三倍。     

Cu与Cu~(2+)反歧化条件的探讨

本文探讨了 Cu 与 Cu~(2+)在不同 Cl~-浓度下,反应终点的颜色、产物及稀释时得到 CuCl 白色沉淀的实验条件。     

Factor analysis regression

The paper describes two regression models—principal components and maximum-likelihood factor analysis—which may be used when the stochastic predictor varibles are highly intereorrelated and/or contain measurement error. The two problems can occur jointly, for example in social-survey data where the true (but unobserved) covariance matrix can be singular. Departure from singularity of the sample dispersion matrix is then due to measurement error. We first consider the more elementary principal components regression model, where it is shown that it can be derived as a special case of (i) canonical correlation, and (ii) restricted least squares. The second part consists of the more general maximum-likelihood factor-analysis regression model, which is derived from the generalized inverse of the product of two singular matrices. Also, it is proved that factor-analysis regression can be considered as an instrumental variables estimator and therefore does not depend on whether factors have been “properly” identified in terms of substantive behaviour. Consequently the additional task of rotating factors to “simple structure” does not arise.     

右π—逆半群的最小群同余

本文具体给出了右逆半群的最小群同余的最简表达形式.     

矩阵的广义逆与线性方程组的反问题

本文讨论了矩阵的广义逆的若干性质，并利用一类特殊的广义逆──左逆，给出了求解线性方程组的反问题和一般性方法．