基于最佳线性无偏估计的模型权数的小域估计

文章介绍了一种基于EBLUP的模型权数的小域估计方法.这种估计方法一方面使小域的目标估计量是加权线性组合,从而使估计过程以及均方误的估计更加简单;另一方面得到的估计量不依赖于模型的假定,是一种稳健的估计量.文章还通过一个简单的模拟案例说明了这种估计量的稳健的性质,说明这种估计方法是一种非常符合实际调查情况的小域估计方法.     

通过对辅助变量的线性转化来改进比率估计

一、问题的提出在抽样调查中,比率估计方法是一种普遍应用的估计方法。在实践中,我们往往根据总体及辅助信息的特点建立不同的比率模型,然后再从该模型中得出不同的比率估计量。下面我们考虑一种最常用的比率模型ξ:假设x1,…,xN是已知的辅助变量值(都大于零),y1,…yN为未知的研究变量值,且总体单元总数为N。对于任意给定的xk,有以下关系yk=βxk εk同时对于所有的k∈K,满足Eξ(yk)=βxkVξ(yk)=σ2xk其中β和σ2为未知参数。在抽样总体满足该比率模型的前提下,进行简单随机抽样,可以得到一个非常经典的关于总体总值ty的比率估计量t^yra=…     

整群抽样设计效应的估计

一、引言设计效应是抽样理论中的一个重要概念 ,它被定义为Deff=所考虑抽样设计下估计量的方差相同样本量简单随机抽样估计量的方差设计效应有两个作用 ,一是比较不同抽样设计的效率 ,二是利用简单随机抽样设计的样本量确定满足相同精度要求的复杂抽样设计所需样本量。由于估计     

一类半参数可变系数广义线性模型及其拟合

一、引言1972年 ,Nelder和Wedderburn[1 ] 对经典线性回归模型作了进一步的推广 ,并且提供了一个统一的估计理论和计算框架 ,这个推广的模型就称为广义线性模型 ,在统计学中产生了重要的影响。定义 1　设Yi 为一随机变量 ,如果其密度函数 (连续型时为分布密度、离散型时为概率分布列 )f(yi,θi,i)可表为 :f(yi,θi,i) =exp[yiθi -b(θi)a(i) +c(yi,i) ];则称Yi 服从具有参数θi 和i 的指数分布族分布 ,其中a(·)、b(·)、c(· ,·)为已知函数 ,θi 称为自然参数 ,i 称为多余参数 (nuisanceparameter)。在一定的正则条件下 ,…     

广义部分线性单指数模型的惩罚样条估计

 本文讨论了指数族广义部分线性单指数模型(Generalized Partially Linear Single Index Models, GPLSIM) 的惩罚样条迭代估计,提出了基于惩罚似然和一组预先取定的单指数参数向量 的初始估计的迭代估计算法。另外本文还通过一组模拟数据的分析对所提出的迭代算法进行了验证。     

一种无偏组合预测方法及其贝叶斯模型

一种无偏组合预测方法及其贝叶斯模型①①本项研究系国家教委优秀年轻教师基金资助项目。曾勇唐小我ＡＢＳＴＲＡＣＴＴｈｉｓｐａｐｅｒｄｉｓｃｕｓｓｅｓｓｅｖｅｒａｌｍｅｔｈｏｄｓｔｏｔｅｓｔｕｎｂｉａｓｅｄｎｅｓｓｉｎｆｏｒｅｃａｓｔｍｏｄｅｌｓ,ｔｈｅｎ...     

线性相关模型及其估计

线性相关模型及其估计雷钦礼本文针对经济和社会研究领域中相关变量及其观测数据的特点并吸收回归分析中模型描述分析的思想，提出相关模型描述分析方法，用于讨论线性相关模型及其估计方法。一、两变量线性相关模型与估计假设两个线性相关的随机变量为Ｘｆｌｌｙ，其样本...     

时间数列模型的联合估计

月份或季度资料时间数列,至少存在长期趋势、季节变动和不规则变动三种变动。测定和分解这三种变动,是时间数列分析的基本任务之一。目前,国内外通行的测定方法是分别测定,即用移动平均法或曲线配合法测定出长期趋势,再用移动平均趋势剔除     

线性回归模型与对数线性回归模型的优选——几种简便的检验方法的运用

回归分析是进行统计预测、描述,评价经济变量间关系及进行政策模拟的一种重要方法。在进行回归分析时,一个重要的问题是模型的优选。一方面是在模型形式一定的情况下选择自变量(即在所有可能自变量中选择出最佳的自变量组合),另一方面是模型形式的选择。 在回归分析中,最简单的模型是线性回归模型:     

非均衡经济计量模型及其估计

非均衡经济计量模型是在经济计量理论和非均衡市场大量统计观察的相互作用下发展起来的。它的开创者是美国经济计量学家费阿和杰斐。 一、基本模型 假设需求方程和供给方程如下。需求方程 Dt== a0X_t~D μ_t~D (t=1,2,…,T)(1)供给方程 St=β_0X_t~sX_t~s μ_t~s (t=1,2,…,T)(2)这里,Dt表示时期t的需求量,St表示时期t的供给量,X_t~D、X_t~s是各种外生变量的向量,a0,β0是待估参数,μ_t~D,μ_t~s是随机误差项,并假设μ_t~D,μ_t~s的均值为0方差为常数,无序列相关、     

The GMDH Algorithm of Ivakhnenko

In 1966, the Russian cyberneticist, A.G. Ivakhnenko, introduced a technique for constructing an extremely high-order regression-type polynomial. The algorithm, the Group Method of Data Handling (GMDH), builds a multinomial of degree in the hundreds, whereas standard multiple regression becomes bogged down in computation and linear dependence. The GMDH method is ideal for complex, unstructured systems where the investigator is only interested in obtaining a high-order input-output relationship. Also, the Ivakhnenko algorithm is heuristic in nature and is not based on a solid foundation as is regression analysis.     

Local Linear Estimation of Second-Order Diffusion Models

In this article, we present the local linear estimations for diffusion coefficient and drift coefficient in the second-order diffusion model. We show that under mild conditions, the estimators are weak consistent. We also use a Monte Carlo experiment to compare our estimators with the ones in Nicolau (2007 Nicolau , J. ( 2007 ). Nonparametric estimation of scend-order stochastic differential equations . Econometric Theor. 23 : 880 – 898 .[Crossref], [Web of Science ®] , [Google Scholar]).     

The Superiorities of Bayes Linear Minimum Risk Estimation in Linear Model

In this article, the Bayes linear minimum risk estimator (BLMRE) of parameters is derived in linear model. The superiorities of the BLMRE over ordinary least square estimator (LSE) is studied in terms of the mean square error matrix (MSEM) criterion and Pitman closeness (PC) criterion.     

Jackknife Estimation for Smooth Functions of the Parametric Component in Partially Linear Regression Models

Abstract

It is known that due to the existence of the nonparametric component, the usual estimators for the parametric component or its function in partially linear regression models are biased. Sometimes this bias is severe. To reduce the bias, we propose two jackknife estimators and compare them with the naive estimator. All three estimators are shown to be asymptotically equivalent and asymptotically normally distributed under some regularity conditions. However, through simulation we demonstrate that the jackknife estimators perform better than the naive estimator in terms of bias when the sample size is small to moderate. To make our results more useful, we also construct consistent estimators of the asymptotic variance, which are robust against heterogeneity of the error variances.     

Estimation in Singular Linear Models with Stochastic Linear Restrictions

This article generalizes the ordinary mixed estimator (OME) in theory, and obtains the estimator of the unknown regression parameters in singular linear models with stochastic linear restrictions: singular mixed estimator (SME). We also give some properties of SME obtained in this article, and prove that it is superior to unrestricted least squared estimator (LSE) in singular linear models in the sense of the covariance matrix and generalized mean square error (GMSE). After that, we also have a discussion about the two-stage estimator of SME. The result we give in this article could be regarded as generalizations of both OME and unrestricted LSE at the same time.     

A Discrete Time Parametric Model for the Analysis of Failure Time Data

This paper introduces a parametric discrete failure time model which allows a variety of smooth hazard function shapes, including shapes which are not readily available with continuous failure time models. The model is easy to fit, and statistical inference is simple. Further, it is readily extended to allow for differences between subjects while retaining the ease of fit and simplicity of statistical inference. The performance of the discrete time analysis is demonstrated by application to several data sets.     

The Partial Linear Model in High Dimensions

Partial linear models have been widely used as flexible method for modelling linear components in conjunction with non‐parametric ones. Despite the presence of the non‐parametric part, the linear, parametric part can under certain conditions be estimated with parametric rate. In this paper, we consider a high‐dimensional linear part. We show that it can be estimated with oracle rates, using the least absolute shrinkage and selection operator penalty for the linear part and a smoothness penalty for the nonparametric part.     

Ridge Estimation to the Restricted Linear Model

This article is concerned with the problem of multicollinearity in a linear model with linear restrictions. After introducing a spheral restricted condition, a new restricted ridge estimation method is proposed by minimizing the sum of squared residuals. The property of the new estimator in its superiority over the ordinary restricted least squares estimation is then theoretically analyzed. Furthermore, a sufficient and necessary condition for selecting the ridge parameter k is obtained. To simplify the selection of the ridge parameter, a sufficient condition is also given. Finally, a numerical example demonstrates the merit of the new method in the aspect of solving the multicollinearity over the ordinary restricted least squares estimation.     

Minimax Empirical Bayes Estimators in Multivariate Mixed Linear Models with Unequal Replications

Predictive influence of explanatory variables has been studied in both univariate and multivariate distributions. In the Bayesian approach, the same problem is considered in absence of multicollinearity in the dataset. The aim of this article is to study the same in the presence of perfect multicollinearity. To do this, we first derived the predictive distributions for full model and reduced model using vague prior density. Then the discrepancies between these predictive distributions are measured by the Kullback–Leibler (K–L) directed measure of divergence to assess the influence of deleted explanatory variables. Finally, distribution of the discrepancies is derived and the test procedure is performed.     

Risk Comparison of Inequality Constrained Estimators in the Heteroscedastic Linear Model

There exist many studies which treat the inequality and/or interval constraints on coefficients in the homoscedastic linear regression model. However, the sampling performance of the inequality constrained estimators in the heteroscedastic linear model has not been examined. This paper considers the inequality constrained estimators in the heteroscedastic linear regression model and derives their risks under a quadratic loss function. Furthermore, using the inequality constrained estimators, we introduce a pre-test estimator which might be employed after the test for homoscedasticity and derive its risk. In addition, the risk performance of these estimators is evaluated numerically.