小域的双重稳健估计方法

小域估计问题是抽样调查的热点问题之一,其主流发展方向是基于模型的估计方法。但是,这种方法依赖于模型的假定,若调查数据满足模型的假定条件,估计的效果会非常好;反之,无法得到有效的估计量。文章利用Box—Cox变换和抽样设计权数得到小域的双重稳健估计量;并通过模拟例子,说明这种方法是一种双重稳健的小域方法。     

多目标变量调查的小域的稳健估计量研究

大型的抽样调查不仅是多目标的复杂调查,而且在估计总体目标变量的基础上还需要对其中的一些域的目标变量进行估计,所以小域估计和多目标估计问题一直是抽样调查的热点问题.文章主要利用模型校准权数的方法,解决小域中的多目标估计问题,并得到小域的多个目标变量的稳健估计量.     

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.     

分位数回归模型在小域估计中的应用

小域估计问题日益受到社会各界的关注,它通常利用辅助信息和统计模型提高估计的精度。其中最常用的小域模型是混合模型,即利用域随机效应来解释域间变化,但是这种模型要求严格的假定条件,不易于处理实际中存在异常值或重尾现象的小域估计问题。本文将分位数回归模型引入小域估计中,这个模型不需要强的假定条件,可以处理实际中存在异常值或是重尾现象的小域估计问题,并通过一个模拟案例进一步说明了基于分位数回归模型的小域估计方法可以得到更加稳健的估计量．挖掘更多的信息来提高小域估计的精度,是一种比较好的小域估计方法。     

基于空间模型的小域估计方法

小域估计成为当今抽样调查的热点问题之一,日益受到社会各界的关注。小域估计多采用基于模型的估计方法,其中以线性混合模型最为普遍,这种模型通常假定域随机效应是独立的。但是,在实际各个域之间往往表现出一定的空间相关性,并且这种相关性随着距离的增加而减小,若忽视这种空间效应,估计的精度会大大的降低。本文运用域随机效应为空间相关的空间模型来解决空间数据下的小域估计问题,并用基于这种空间模型的权数的方法得到了目标变量的稳健估计量,很大程度上提高小域估计的精度,是一种比较好的小域估计方法。     

小域估计的理论和最新进展

小域估计问题是当今抽样调查中的一个热点问题,由于小域样本量很小甚至为零,用传统的直接估计无法得到小域的精确估计,故借助于其他相邻与相似的小域的样本信息和历史信息的间接估计来提高估计的精度,是十分必要的.目前小域估计的主流发展方向是基于模型的小域估计方法,在介绍基于小域层次模型的小域估计方法和基于单元层次模型的小域估计方法的理论基础上,对实际调查中存在的一些小域估计问题以及针对这些实际问题的最近进展进行介绍,具有重要的理论和实践意义.     

基于γ散度的单元水平模型小域稳健估计

在基于抽样调查数据对总体参数进行估计的方法中,小域估计方法能够借助于辅助信息对小样本乃至无样本区域的参数进行有效的估计,并被广泛应用于抽样估计领域。单元水平模型作为小域估计的基本模型之一,是处理单元级别数据估计的有力工具之一。在单元水平模型的应用条件中,需假定区域随机误差和模型随机误差均服从正态分布。然而,在抽样调查中,满足这一条件的调查数据是很少的,尤其是在观测数据中出现离群值时。不满足正态性假设条件下的小域估计量会产生较大的偏差和均方误,因此有必要研究针对正态性假设和离群观测值不敏感的稳健估计方法。通过引入γ散度和γ似然函数,构建了基于单元水平模型的小域稳健估计方法,得到了模型参数的稳健估计和小域目标变量的稳健估计。与现有的稳健估计方法相比,所提新方法能更好地处理区域随机误差和模型随机误差非正态的情形,对于目标变量存在离群观测的情形,具有更好的稳健性,估计均方误更小。在利用模拟数据进行验证中,比较了不同误差分布情形下几类常用估计方法得到的估计量的均方误差,并进一步探究了随着污染分布的方差和比率变化,所得估计量的均方误差变化情形。最后,通过应用于经典的小域估计数据,进一步验证了所提新...     

域与小域估计理论的综述

抽样调查领域中,为满足多层次的需求产生了域与小域估计的理论与方法.文章介绍域与小域估计的理论,并综述相关文献.     

遥感辅助的农作物种植面积小域估计方法研究

遥感影像是大数据的一种,利用遥感对农作物播种面积进行估算常采用回归估计量或校准估计量,通常都需要将地面样本数据与遥感分类信息相结合。但对于大多数回归估计量,对省级总体的农作物面积估算只能满足对省级总体的精度要求而不能分解到更小区域,比如县和乡级。本文利用黑龙江省2011年的地面实测样本数据结合遥感分类结果,构建了单元层次的多响应变量的多元回归形式的小域模型,并将小域效应设定为固定形式。这样基于回归估计方法,既可以估算分县的主要作物播种面积,也可以使得各县播种面积估计结果相加就等于回归模型含义下的省级总体的总量估计。对黑龙江省玉米、水稻、大豆分县小域估计结果的精度评价（变异系数C.V）,平均而言均可以满足县级精度要求。本文的结果表明小域估计方法在解决省级总体对全省和分县的农作物种植面积多级估算问题中具有很好的应用。     

放回抽样下HT估计量的性质及应用

放回抽样下传统的估计方法是采用Hansen-Hurwitz估计。而放回抽样下HH估计量并不是一致最小方差无偏估计,本文提出了另一种估计方法,即采用Horvitz-Thompson估计,并论证了放回抽样下HT估计量的三条定理,及与HH估计量的比较。然后以放回简单随机抽样和PPS抽样为例,通过理论公式、计算机模拟以及具体案例,进行更具体的分析。说明在一定条件下,HT估计量相对更优。在实际应用中,本文也提出了通过比较方差估计作为选取估计量的准则。     

Robust estimation for order of hidden Markov models based on density power divergences

In this paper, we study the robust estimation for the order of hidden Markov model (HMM) based on a penalized minimum density power divergence estimator, which is obtained by utilizing the finite mixture marginal distribution of HMM. For this task, we adopt the locally conic parametrization method used in [D. Dacunha-Castelle and E. Gassiate, Testing in locally conic models and application to mixture models. ESAIM Probab. Stat. (1997), pp. 285–317; D. Dacunha-Castelle and E. Gassiate, Testing the order of a model using locally conic parametrization: population mixtures and stationary arma processes, Ann. Statist. 27 (1999), pp. 1178–1209; T. Lee and S. Lee, Robust and consistent estimation of the order of finite mixture models based on the minimizing a density power divergence estimator, Metrika 68 (2008), pp. 365–390] to avoid the difficulties that arise in handling mixture marginal models, such as the non-identifiability of the parameter space and the singularity problem with the asymptotic variance. We verify that the estimated order is consistent and simulation results are provided for illustration.     

Estimators of shift based on statistics of the Kolmogorov-Smirnov type

This paper is concerned with the estimation of a shift parameter δ_o, based on some nonnegative functional Hg₁ of the pair (D^δ_N(x), f?^δ_N(x)), where D^δ_N(x) = K_N/b {F_2,n(x)—F_1,m (x + δ)}, +^δ_N(x) = {mF_1,m (x + δ) + nF_2,n(x)}/N, where F_1,m and F_2,n are the empirical distribution functions of two independent random samples (N = m + n), and where K²_N = mn/N. First an estimator δ_N, is defined as a value of δ minimizing a functional H of the type of H₁. A second estimator δ¹_N is also defined which is a linearized version of the first. Finite and asymptotic properties of these estimators are considered. It is also shown that most well-known test statistics of the Kolmogorov-Smirnov type are particular cases of such functionals H₁. The asymptotic distribution and the asymptotic efficiency of some estimators are given.     

Estimators of location based on Kolmogorov-Smirnov-type statistics

Two classes of estimators of a location parameter ø₀ are proposed, based on a nonnegative functional H₁^* of the pair (D₁^ø_N, G^ø_N), where and where F_N is the sample distribution function. The estimators of the first class are defined as a value of ø minimizing H₁^*; the estimators of the second class are linearized versions of those of the first. The asymptotic distribution of the estimators is derived, and it is shown that the Kolmogorov-Smirnov statistic, the signed linear rank statistics, and the Cramérvon Mises statistics are special cases of such functionals H₁^*;. These estimators are closely related to the estimators of a shift in the two-sample case, proposed and studied by Boulanger in B2 (pp. 271–284).     

New Results on the Small-Sample Properties of Some Robust Univariate Estimators of Location

This article compares eight estimators in terms of relative efficiencies with the univariate mean, some of which have not been compared previously. Four estimators, when testing hypotheses, are compared in terms of actual Type I errors. In terms of point estimation, the modified one-step M-estimator, one-step M-estimator, and rfch estimator are found to be the three best choices depending on the proportion of outliers. In terms of actual Type I errors, the modified one-step M estimator's and rfch estimator's level was between.045 and.055 in 5 out of 7 situations when real data were used in simulations.     

The Research on Two Kinds of Restricted Biased Estimators Based on Mean Squared Error Matrix

Sakall?oglu et al. (2001 Sakall?oglu , Kaç?ranlar , Akdeniz ( 2001 ). Mean squared error comparisons of some biased estimators . Commun. Statist. Theor. Meth. 30 : 347 – 361 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) dealt with the comparisons among the ridge estimator, Liu estimator, and iteration estimator. Akdeniz and Erol (2003 Akdeniz , F. , Erol , H. ( 2003 ). Mean squared error matrix comparisons of some biased estimators in linear regression . Commun. Statist. Theor. Meth. 32 : 2389 – 2413 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) have compared the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean squared error sense. In this article, we study the ridge estimator and Liu estimator with respect to linear equality restriction, and establish some sufficient conditions for the superiority of the restricted ridge estimator over the restricted Liu estimator and the superiority of the restricted Liu estimator over the restricted ridge estimator under mean squared error matrix, respectively. Furthermore, we give a numerical example.     

Robust m-estimators

This paper provides a summary of the influence function approach to robust estimation of parametric models. Hampel's optimality results for M-estimators with a bounded influence function is generalized to allow for arbitrary choices of the asymptotic efficiency criterion and the norm of the influence function. Further extensions to other cases of practical interest are also considered.     

抽样调查中基于平衡样本的稳健预测

抽样调查中基于模型推断方法获得的估计量性质是依赖于模型的。在恰当的模型下比率估计和扩张估计是最优线性无偏估计。当模型设定错误时,比率估计和扩张估计是有偏估计,但如果样本是平衡的,可以消除偏倚,从而实现了复杂问题简单处理的思想。     

Stable estimation of location parameter -nonasymptotic approach

Let X₁:, X₂:, …, X_n be iidrv's with cdf F?, F?(x)=F (x-θ), R. Let T be an equivariant median-unbiased estimator of θ. Let πε(F)={G = (1 -ε) F+εH, H any cdf} and let M(G, T) be a median of T if X₁ has cdf G. The oscillation of the bias of T, defined as

Bε(T)=sup (M(G₁ T) :G₁,G₂:∈π_σ:(F)} ,is considered and the estimator with the smallest B$epsi;(T) is explicitly constructed     

Small area estimation of proportions in business surveys

Binary data are often of interest in business surveys, particularly when the aim is to characterize grouping in the businesses making up the survey population. When small area estimates are required for such binary data, use of standard estimation methods based on linear mixed models (LMMs) becomes problematic. We explore two model-based techniques of small area estimation for small area proportions, the empirical best predictor (EBP) under a generalized linear mixed model and the model-based direct estimator (MBDE) under a population-level LMM. Our empirical results show that both the MBDE and the EBP perform well. The EBP is a computationally intensive method, whereas the MBDE is easy to implement. In case of model misspecification, the MBDE also appears to be more robust. The mean-squared error (MSE) estimation of MBDE is simple and straightforward, which is in contrast to the complicated MSE estimation for the EBP.