广义偏最小二乘(PLS)估计类

本文研究了一类含有偏最小二乘（partialleastsquaresPLS）估计的估计类．给出了PLS估计的一般代数形式；讨论了含有PLS估计的广义PPLS估计类的统计性质；给出了该估计类优于最小二乘估计的条件．     

对部分线性模型用惩罚最小二乘估计时最优光滑化的注记

部分线性模型也就是响应变量关于一个或者多个协变量是线性的, 但对于其他的协变量是非线性的关系\bd 对于部分线性模型中的参数和非参数部分的估计方法, 惩罚最小二乘估计是重要的估计方法之一\bd 对于这种估计方法, 广义交叉验证法提供了一种确定光滑参数的方法\bd 但是, 在部分线性模型中, 用广义交叉验证法确定光滑参数的最优性还没有被证明\bd 本文证明了利用惩罚最小二乘估计对于部分线性模型估计时, 用广义交叉验证法选择光滑参数的最优性\bd 通过模拟验证了本文中所提出的用广义交叉验证法选择光滑参数具有很好的效果, 同时, 本文在模拟部分比较了广义交叉验证和最小二乘交叉验证的优劣.     

推广的生长曲线模型中未知参数矩阵的广义最小二乘估计的可容许性

本文在设计矩阵与结构矩阵分别正交的条件下,研究了推广的生长曲线模型未知参数矩阵的广义最小二乘估计.运用矩阵理论证明了此广义最小二乘估计在某个线性估计类中的可容许性.并对潘建新(1989)的结果的推广.     

多元广义岭估计及K值选以的Q（c）准则

当自变量间存在复共线性时，最小二乘估计就表现出不稳定并可能导致错误的结果。本采用广义岭估计β（K）来估计多元线性模型的回归系数β=vec(B),通过岭参数K值的选取 ，可使广义岭估计的均方误差MSE小于最小二乘估计的MSE。指出了广义岭估计中根据MSE准则选取K值存在的主要缺陷，采用了一种选取K值的新准则Q（c），它包含MSE准则和最小二乘LS准则作为特例，从理论上证明和讨论了Q（c）准则的优良性，阐明了c值的统计 含义，并给出了确定c值的方法。     

部分线性单指标模型参数部分的统计推断

考虑部分线性单指标模型参数部分的统计推断问题.主要研究利用剖面最小二乘法（profile least-squares technique）估计模型的未知参数和函数,并利用该估计建立模型中参数部分的广义似然比（generalized likelihood ratio,GLR）检验统计量.在原假设条件下,文中新提出的GLR检验统计量渐近服从具有尺度常数（scaleconstant）与自由度独立于讨厌参数（nuisance parameters）的χ^2-分布,这一现象被称为Wilks现象.最后给出数字模拟与实际例子,验证文中所提出的检验方法.     

回归函数的速归LS─权估计的强收敛性

本文讨论了把传统的最小二乘方法与非参数的权函数法结合起来所得回归函数的递归最小二乘—权估计（简记为ＬＳ—权估计）的强收敛性。     

回系数的广义根方估计及其模拟

文献［１，２］中提出了回归系数的根方估计β＾（ｋ），当回归自变量间存在复共线关系时，β＾（ｋ）较回归系数的最小二乘估计β有所改善。本文将根方估计作一拓广，得出了回归系数的广义根方估计β＾（Ｋ），其中Ｋ为对角阵。文中证明了广义根方估计β＾（Ｋ）较β＾（ｋ）能更有效地改善最小二乘估计，并给出了广义根方估计的显式解，在此基础上，提出了广义根方估计的显式解和一种确定ｋｉ的方法。     

线性模型参数的聚集改进广义Liu估计的相对效率

对于聚集数据的线性模型,给出了参数β的聚集改进广义Liu估计,研究了该估计相对于最小二乘估计及相对于Peter—Karsten估计的两种相对效率,并得到了相对效率的上界.实例分析表明,聚集改进广义Liu估计比最小二乘估计、Peter—Karsten估计更有效.     

门限自回归模型参数最小二乘估计的强收敛速度

本文在给定门限自回归模型阶数、门限和延迟参数的情况下，证明了一般门限自回归模型参数和残差方差的最小二乘估计的强收敛速度为Ｏ（（ｌｏｇｌ９ｏｇｎ／ｎ）１／２），并证明了残差方差的最小二乘估计具有渐近正态性．     

关于EV线性回归模型中的广义最小二乘估计

本文考虑EV（errors-in-variables）线性模型．在一般的条件下证明了广义最小二乘估计的强收敛和渐近正态性，然后在小样本意义下给出了模拟结果．     

Mixed Estimations and Bayes Estimation of theRegression Coefficient in Multivariate Linear Model

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In this paper an efficient estimation methodology for the partially linear models with random effects is proposed. For this, we use the generalized least square estimate (GLSE) and the B-splines methods to estimate the unknowns, and employ the penalized least square method to obtain the estimators of the random effects item. Further, we also consider the estimation for the variance components. Compared with the existing methods, our proposed methodology performs well. The asymptotic properties of the estimators are obtained. A simulation study is carried out to assess the performance of our proposed methodology.     

生长曲线模型中参数的Bayes线性无偏估计

本文在平方损失下导出了生长曲线模型中参数的Bayes线性无偏估计(LUE), 并在均方误差矩阵(MSEM)准则下研究了Bayes LUE相对于广义最小二乘估计(GLSE)的优良性. 对于非满秩情形,获得了可估函数的Bayes LUE并讨论了其优良性问题.     

A method for approximations to the pdf'S and cdf'S of GLSE's and its application to the seemingly unrelated regression model

This paper first develops a valid method for approximations to the pdf's and cdf's of GLSE in linear models and, applying this method to the Zellner estimator with an unrestricted sample covariance in the seemingly unrelated regression model, obtains an approximate pdf with a bound of ordern ⁻² and an approximate covariance matrix with a bound of ordern ⁻³ This research was done at the London School of Economics while the authors were British Council scholars. Kariya is grateful to Professor J. Durbin for a general discussion on asymptotic expansions. Further the authors deeply appreciate Professor Y. Kataoka and anonymous referee for their invaluable comments and suggestions.     

以多辅助指标线性组合为辅助信息的比估计法

本文以提高估计量的精度为目的,把多个辅助变量适当加权构造了一个单辅助变量,利用构造的单辅助指标定义了一个新的比估计量,从理论上研究了这种辅助指标组合中权w_k的选取方法.并将这种新构造的比估计量与单辅助指标比估计量、Srivastava及B.Kiregyera链式比估计量在精度上进行了数值比较,结果表明:这种新的多辅助指标组合比估计在精度上要优于以上几种比估计.     

Computational estimation skill of preservice teachers: operation type and teacher view

Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers’ estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the meaning of estimation and the importance of teaching it. Three sets of instruments were used: an estimation task, a computational task, and a belief survey. Results indicated that PSTs performed differently depending on the types of operations on the estimation test. It was also found that different types of problems elicited different strategies. Furthermore, the intervention of the study, along with five other factors were found to significantly correlate with estimation skills. The five factors include PSTs’ mathematical knowledge, their reported confidence about estimation skills, their self-reported knowledge about calculator use in instruction, their views of estimation in teaching mathematics, and their definition of estimation. A negative correlation was documented for the knowledge of calculator use in instruction, and positive correlations were present for other factors. Implications are discussed in accordance with these findings.     

带线性约束的回归模型参数估计的新研究

针对一般带约束的最小二乘估计(ORLSE)在参数估计中处理复共线性的不足,引入随机线性约束,提出了约束k-d估计方法。在均方误差(MSE)下,讨论了它的性质,得到了四个主要结果,与带约束的最小二乘估计ORLSE、约束岭估计(RRE)和约束型Liu估计比较,得出更好的结论。     

生长曲线模型的惩罚最小二乘估计

主要考虑了生长曲线模型中的参数矩阵的估计.首先基于Potthoff-Roy变换后的生长曲线模型,采用不同的惩罚函数:Hard Thresholding函数,LASSO,ENET,改进LASSO,SACD给出了参数矩阵的惩罚最小二乘估计.接着对不做变换的生长曲线模型,直接定义其惩罚最小二乘估计,基于Nelder-Mead法给出了估计的数值解算法.最后对提出的参数估计方法进行了数据模拟.结果表明自适应LASSO在估计方面效果比较好.     

Examining and developing fourth grade children’s area estimation performance

This study explored children’s area estimation performance. Two groups of fourth grade children completed area estimation tasks with rectangles ranging from 5 to 200 square units. A randomly assigned treatment group completed instructional sessions that involved a conceptual area measurement strategy along with numerical feedback. Children tended to underestimate areas of rectangles. Furthermore, rectangle size was related to performance such that estimation error and variability increased as rectangle size increased. The treatment group exhibited significantly improved area estimation performance in terms of accuracy, as well as reduced variability and instances of extreme responses. Area measurement estimation findings are related to a Hypothetical Learning Trajectory for area measurement.