回归估计

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

Based on the autoregression equation for the standard variation of the residual errors obtained by ordinary regression analysis, the least square estimates and the maximum likelihood estimates for the regression, the autoregression and the moving average coefficients are derived.

提出一种异方差回归－时序模型，通过建立回归分析残差的标准差自回归方程，给出回归系数、自回归系数和滑动平均系数的最小二乘估计和极大似然估计。

Especially, by an example for analysis of the authoritical boston housing prices data, we emphasize on applying an new regression model and method -- semiparametric functional coefficient quantile regression and two-step estimation method to show the great explaination of the new

介绍了非参数回归和半参数回归的发展历程及其估计方法，还介绍了分位数回归的相关理论及其研究现况。在半参数、变系数回归和分位数回归的基础上，进一步讨论了非参数和半参数的变系数分位数回归模型和局部多项式线性估计法。

We make the following assumption for When 2 is positive definite matrix, different estimators about matrix of regression coefficients and inefficiency of Least squares estimate have been discussed in many documents. Considered 2 is nonnegative definite matrix, this thesis derives Best linear unbiased Estimate of parameter matrix B and estimable parameter function KBL under the meaning of matrix nonnegative definite and the property of maximum probability of BLUE is investigated.

当∑＞0时，众多文献讨论了回归系数阵的各种估计及LSE的有效性，本文考虑了当∑≥0的情形，给出了回归系数阵B及其可估参数函数KBL的在矩阵非负定意义下的最优估计，研究了它的一个最大概率性质，并且讨论了最小二乘估计成为最佳线性无偏估计的充分必要条件，在此基础上给出了均值矩阵的最小二乘估计与BLUE的偏差估计，定义了LSE相对于BLUE的一个相对效率，并给出了它的界。

In chapter 1, regression models with censored data, LSE for censored regression models and LAD estimation for models with fixed censoring point are introduced. Then, we state our main results for LAD estimator of nonlinear regression models with randomly censored data, including consistency, boundedness in probability and asymptotic normality. The proofs of our main theorems are given in detail. In chapter 2, we state the main difficulty of obtaining numerical solution for censored LAD estimation, and recall the history of studies on this problem including some anterior algorithms.

在第一章，首先介绍删失线性回归模型的基本概念和性质，并对已有的估计方法，如最小二乘估计、固定点删失的最小一乘估计等做了简单的回顾；然后，把固定点删失线性回归模型的最小一乘估计方法推广到了随机删失、非线性模型的情形，并得到了估计量的一些渐近性质，如相合性、渐近正态性等；最后，给出主要结果的详细证明过程。

Ects, the covariance matrix of observation vector has special structure,and using the linear transformation for original model by idempotent matricesin the spectral decomposition of the covariance matrix, the problem of estima-tion of the covariance matrix becomes simultaneous estimation of all the distincteigenvalues of it.

在带有随机回归系数的一般线性模型中，首次提出了随机回归系数和参数的Minimax估计问题，分别在齐次线性估计类和一切估计类中研究了一个线性估计的Minimax性。

In Chapter 2, the Balanced LS Estimation is defined for the linear model when its error covariance is positive definite or singular. The new estimation as well as the necessary and sufficient conditions is gained for its unbiasedness, efficiency and admissibility.

第2章提出了一般线性回归模型和奇异线性回归模型平衡LS估计的概念，得到回归系数β的平衡LS估计，进而探讨了这种估计的无偏性、有效性和可容许性。

E. , regression problems with design variable taking values on the surface of unit sphere.

这种涉及变量之间相互关系的回归估计问题具有更重要的实际意义。

As one of the leading branches of the modern statistics, the riouparametric regression analysis is widely applied to explore the relationship between the the response variable y and the covariable A'.

对于非参数回归人们提出了许多估计方法，如核估计，局部多项式估计，光滑样条估计，级数估计(傅里叶级数估计，小波级数估计)等。这些方法本质上讲都是局部估计或局部光滑，当回归变量X为一维变量时，非参数回归函数用这些方法一般都能得到很好的估计。

The aim of this study is to quantitatively investigate the effects of both temperature and photosynthetically active radiation on the leaf growth of greenhouse cucumber.

该模型对黄瓜叶面积指数的模拟结果与1∶1直线之间的决定系数R2和回归估计标准误差RMSE分别为0.8792和0.3980，比用积温法和比叶面积法模拟叶面积指数的精度分别提高了37%和74%。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。