A generalized inverse regression estimator in multi-univariate linear calibration

A multivariate linear calibration problem, in which response variable is multivariate and explanatory variable is univariate, is considered. In this paper a class of generalized inverse regression estimators is proposed in multi-univariate linear calibration. It includes the classical estimator and the inverse regression one (or Krutchkoff estimator). For the proposed estimator we derive the expressions of bias and mean square error (MSE). Furthermore the behavior of these characteristics is investigated through an analytical method. In addition through a numerical study we confirm the existence of a generalized inverse regression estimator to improve both the classical and the inverse regression estimators on the MSE criterion.     

“动＋个＋……”中“个”的句法语义分析

“个”是使用频率最高的量词,与词类的搭配相当自由。“动 个 ……”中“个”后面的成分既可能是一般的可个称的体词性词语,也可能是抽象的不可个称的体词性词语,还可能是表示动作行为和性质状态的谓词性词语。如果“个”后是一般的可个称的体词性词语,大家一致同意“个”为量词,这时的“个”与其他位置上的“个”无异。可是,如果“个”后是抽象的不可个称的体词性词语或谓词性词语,人们的观点不太一致。作者用普通话、方言和古语相结合、印证的办法,得出“动 个 ……”中“个”后无论是体词性词语还是谓词性词语,“个”都是量词,同时也指出这一位置上的“个”在表意上有别于其他位置上的“个”。     

基于逆高斯分布的项目投资风险收益理论模型

项目投资经济效果评价指标的风险分析指的是如何依据各影响因素的概率分布来推求经济效果评价指标的概率分布.本文从理论上建立了基于逆高斯分布项目投资风险收益理论模型并给予精细的分析.这对提高项目投资经济的可靠性及风险分析理论具有重要意义.     

基于非线性偏最小二乘的操作臂逆解算法

操作臂逆运动学问题是机器人控制中的一项重要内容。目前使用较多的神经网络法大多为多输入多输出或者 多输入单输出方式,需要大量运算。非线性偏最小二乘法( NLPLS)建立的模型分为内部和外部模型,样本数据经外部模 型处理后才用于训练若干个单输入单输出的神经网络。对PUMA560操作臂的仿真试验表明,在相同隐层神经元数的情 况下,该算法比普通神经网络法具有更好的预测精度。这也表明,NLPLS只需较少的隐层神经元数就可以达到普通方法 的精度,从而减少运算量。     

有关P_B~⊥P_A、P_A~⊥P_B的矩阵等式和秩等式

在M=(A B)中,令A1=P⊥BPA,B1=P⊥APB,利用投影算子理论和矩阵秩方法可以得到关于A1,B1的一些矩阵等式和秩等式.     

A generalized improvement procedure for variance bounds for minimum variance unbiased estimator in inverse sampling

New bounds are obtained for the variance of the minimum variance unbiased estimator of p i n inverse sampling. A generalized procedure for further improving the bounds is also discussed.     

无阻尼单摆运动方程反函数形式的精确解

利用函数进行变换,将单摆的二阶非线性微分方程化为一阶非线性微分方程进行积分求解,再利用三角函数变换,最后求出用Legendre椭圆积分表示的无阻尼单摆运动方程反函数形式的精确解。     

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,