Equality of two blues and ridge-type estimates

Equality is shown of the g-inverse and Moore-Penrose inverse representation of the BLUE in the general linear model. The proof is based on a matrix identity which allows also to establish a functional relationship between the BLUE and Ridge-type estimates.     

Partial least squares estimator for single-index models

The partial least squares (PLS) approach first constructs new explanatory variables, known as factors (or components), which are linear combinations of available predictor variables. A small subset of these factors is then chosen and retained for prediction. We study the performance of PLS in estimating single-index models, especially when the predictor variables exhibit high collinearity. We show that PLS estimates are consistent up to a constant of proportionality. We present three simulation studies that compare the performance of PLS in estimating single-index models with that of sliced inverse regression (SIR). In the first two studies, we find that PLS performs better than SIR when collinearity exists. In the third study, we learn that PLS performs well even when there are multiple dependent variables, the link function is non-linear and the shape of the functional form is not known.     

A further note on a theorem on the difference of the generalized inverses of two nonnegative definite matrices

Andrews and Phillips (1986) gave a simplified proof for the result that established the nonnegative definiteness of the difference of the Moore-Penrose inverses of two nonoegative definite matrices, a result originally due to Milliken and Akdeniz (1977), The purpose of this paper is to offer a simple proof for a generalization of this result,     

Analysis of a factorial quantal response assay using inverse regression

An inverse regression approach to analyzing quantal response assays with one quanritative independent- variable and any number of qualitative independent variables is presented. A general factorial model ror LQC- inverted relationship and methods of testing hypotheses estimating qulitative Interest are developed. This naper provides a modified method of analysis which is easier to apply than previously existing methods.     

反证法在高等数学证明题中的应用

结合多年工科数学教学实践,通过典型例题,归纳出反证法在高等数学证明题中的应用。这对高等数学课程的教与学都有一定的参考价值。     

人体完整腰椎骨三维运动的测量研究

为了进行人体完整腰椎骨运动的研究，设计并制造了平行光三维运动测量和分析系统．通过平行光测量系统，将每个椎体上三个标志点的运动投影到光屏上，以摄象机动态记录并输入计算机图象处理系统进行数据处理，同时运用刚体运动学原理进行计算，获得人体完整腰椎骨三维运动的运动特征．     

多变量仿射非线性系统的可逆性秩判据

系统的可逆性判别是非线性控制的逆系统方法的关键,为探索可逆性分析的新途径,该文将系统可逆的秩检验法引入到多变量仿射非线性系统中,其实质是将系统的可逆性判定转化为对系统的输出函数及其导数所构成的雅可比矩阵的秩条件分析。文中给出了仿射非线性系统可逆的秩判据定理与证明过程,提出了一种具体的求逆算法,最后,举例对算法进行了验证,通过与微分几何法和逆系统方法的比较说明了秩判据法的有效性。     

DOMAIN ESTIMATION IN FINITE POPULATIONS1

This paper suggests unbiased estimators (UE's) for the size, mean and total of a domain, with specific features, in a given finite population on the basis of simple random sampling without replacement (SRSWOR) continued till a preassigned number of domain members is observed.     

Integrated Square Error Asymptotics for Supersmooth Deconvolution

Abstract.  We derive the asymptotic distribution of the integrated square error of a deconvolution kernel density estimator in supersmooth deconvolution problems. Surprisingly, in contrast to direct density estimation as well as ordinary smooth deconvolution density estimation, the asymptotic distribution is no longer a normal distribution but is given by a normalized chi-squared distribution with 2 d.f. A simulation study shows that the speed of convergence to the asymptotic law is reasonably fast.     

一种瞬变步长LMS自适应滤波算法

基于规一化起动、平滑递推和ＰＬＳ算法导出了一种新的变步长ＬＭＳ算法。文中分析了起动后的平稳连接和提高起始收敛速度的条件，证明了步长因子μ（ｋ）的瞬变特性及其对减小失调噪声的作用。计算机仿真效果较好，支持了理论分析。