地理加权似乎不相关回归模型及其估计

为了刻画时空异质性,文章基于地理加权回归技术和似乎不相关回归方法提出了一种新的空间计量经济学模型——地理加权似乎不相关模型.对于这类模型中的未知系数函数,提出了两种估计方法,第一种方法是利用局部加权最小二乘方法分别估计每个时刻对应的空间变系数模型,第二种方法是广义局部加权最小二乘估计,考虑了同一地点不同时刻误差之间的相关性.     

单指标纵向数据模型的估计

纵向数据是一类重要的相关性数据,广泛出现在诸多科研领域。单指标模型是多元非参数回归中重要的降维方法,在纵向数据下研究单指标模型是统计研究的热点问题。针对纵向数据单指标模型,提出惩罚改进二次推断函数方法来讨论模型的参数和非参数估计问题。该方法利用多项式样条回归方法逼近模型中的未知联系函数,将联系函数的估计转化为回归样条系数的估计,然后构造关于样条回归系数和单指标系数的惩罚改进二次推断函数,最小化惩罚改进二次推断函数便可得到模型的估计。理论结果显示,估计结果具有相合性和渐近正态性,最后得到了较好的数值模拟结果和实例数据分析结果,结果显示该方法适用于半参数纵向模型的参数和非参数估计问题。     

混合地理加权回归模型的统计诊断

混合地理加权回归模型作为一类能简单有效解决空间非平稳问题的数据分析方法已经得到了广泛的应用.在利用该模型分析实际数据时,一个或多个特殊观测点的存在能导致估计结果发生较大改变.为了能有效检测出异常点,系统研究这类半参数模型的统计诊断与影响分析.首先基于数据删除模型定义了参数分量对应的Cook统计量,其次,基于均值漂移模型讨论了异常点的检验问题,构造了相应的检验统计量.     

空间回归模型估计中的最小二乘法

空间回归模型由于引入了空间地理信息而使得其参数估计变得复杂,因为主要采用最大似然法,致使一般人认为在空间回归模型参数估计中不存在最小二乘法。通过分析空间回归模型的参数估计技术,研究发现,最小二乘法和最大似然法分别用于估计空间回归模型的不同的参数,只有将两者结合起来才能快速有效地完成全部的参数估计。数理论证结果表明,空间回归模型参数最小二乘估计量是最佳线性无偏估计量。空间回归模型的回归参数可以在估计量为正态性的条件下而实施显著性检验,而空间效应参数则不可以用此方法进行检验。     

混合再生散度模型的参数估计

随着社会信息化的发展数据的种类越来越多样化,在实际的数据分析中相对于同质总体,异质总体更具有普遍性,所以混合回归模型是最重要的统计数据分析工具之一。再生散度模型是一种比指数族分布更加广泛的分布,适用性更强。基于此,提出混合再生散度模型,对方位参数进行建模,并通过EM算法研究该模型参数的极大似然估计。同时,通过随机模拟和实例研究说明该模型和方法是有效和有用的。     

半参数空间变系数回归模型的两步估计方法及其数值模拟

文章提出了关于半参数空间变系数回归模型的两步估计方法,该方法可得到模型中常值系数估计量的精确解析表达式,广泛的数值模拟表明所提出的估计方法对估计常值系数具有满意的精度和稳定性。     

纵向可加部分线性测量误差模型的渐近估计

基于纵向数据,研究参数部分协变量含有测量误差的可加部分线性测量误差模型的估计问题,提出了用于模型估计的偏差修正的二次推断函数方法,得到参数部分的估计结果具有相合性、渐近正态性,非参数可加函数的估计结果达到最优收敛速度。数值模拟和实例数据分析结果显示,该模型估计方法在同等条件下要优于广义估计方程方法。理论和数值结果显示,偏差修正的二次推断函数可以有效地处理测量误差和个体内相关性,是一个有效的纵向数据和测量误差数据分析工具,具有一定的理论和应用价值。     

有测量误差时空间自回归模型的估计与检验

近年来运用空间计量经济模型进行实证分析的文献都普遍采用空间自回归(SAR)形式的设定,对参数的估计也多采用极大似然(MLE)的方法。在经典多元线性回归模型中,仅有被解释变量的测量误差并不会影响系数估计的一致性。本文证明对于SAR模型,即使仅当被解释变量存在测量误差时,且无论该测量误差是否与模型本身的扰动项相关,普遍采用的MLE都将是不一致的。为此,Hausman型的设定检验被推广到SAR模型中用以判别是否存在被解释变量的测量误差。当零假设被拒绝时,我们说明由Kelejian&Prucha(1998), Lee(2003)提出的二阶段最小二乘法仍然可以得到参数的一致估计。Monte Carlo模拟的结果与我们的理论预期一致。最后我们用一个估计地方环境支出外溢效应的实例说明如何运用本文所提的方法来检验应用空间自回归模型时可能存在的测量误差。     

纵向部分线性变系数EV模型的估计

纵向数据是随着时间变化对个体进行重复观测而得到的一种相关性数据，广泛出现在诸多科学研究领域。在对个体进行观测时，测量误差不可避免，忽略测量误差往往会导致有偏估计。本文利用二次推断函数方法研究关于纵向数据的参数部分和非参数部分协变量均含有测量误差的部分线性变系数测量误差(errors-in-variables, EV)模型的估计问题。利用B样条逼近模型中的未知系数函数，构造关于回归参数和B样条系数的偏差修正的二次推断函数以处理个体内相关性和测量误差，得到回归参数和变系数的偏差修正的二次推断函数估计，然后证明了估计方法和结果的渐近性质。数值模拟和实例数据分析结果显示本文提出的方法具有一定的实用价值。     

异质性空间随机前沿模型的参数估计及应用

经典的随机前沿模型忽略了决策单元之间的空间关联性，无法准确估计效率影响因素相关参数，限制了其适用范围。本文在空间自回归随机前沿模型的基础上，引入效率影响因素，构建出一个异质性空间随机前沿模型，基于极大似然估计法给出模型参数的单步估计策略，提出决策单元技术效率的最优预测量。理论分析证明，模型参数在一定的假设条件下具备一致性；模拟实验表明，参数估计量和技术效率预测量较之经典模型具有更高的估计精度，且会随着样本量的扩大而逐渐提升。本文使用所提出理论方法讨论了我国城市数字普惠金融发展与技术效率水平之间的相关关系，发现两者之间存在显著的正相关关系，同时也印证了模型设定和估计方法的可靠性。     

Outlier Robust Small‐Area Estimation Under Spatial Correlation

Modern systems of official statistics require the estimation and publication of business statistics for disaggregated domains, for example, industry domains and geographical regions. Outlier robust methods have proven to be useful for small‐area estimation. Recently proposed outlier robust model‐based small‐area methods assume, however, uncorrelated random effects. Spatial dependencies, resulting from similar industry domains or geographic regions, often occur. In this paper, we propose an outlier robust small‐area methodology that allows for the presence of spatial correlation in the data. In particular, we present a robust predictive methodology that incorporates the potential spatial impact from other areas (domains) on the small area (domain) of interest. We further propose two parametric bootstrap methods for estimating the mean‐squared error. Simulations indicate that the proposed methodology may lead to efficiency gains. The paper concludes with an illustrative application by using business data for estimating average labour costs in Italian provinces.     

空间回归模型选择的反思

空间计量经济学存在两种最基本的模型:空间滞后模型和空间误差模型,这里旨在重新思考和探讨这两种空间回归模型的选择,结论为:Moran’s I指数可以用来判断回归模型后的残差是否存在空间依赖性;在实证分析中,采用拉格朗日乘子检验判断两种模型优劣是最常见的做法。然而,该检验仅仅是基于统计推断而忽略了理论基础,因此,可能导致选择错误的模型;在实证分析中,空间误差模型经常被选择性遗忘,而该模型的适用性较空间滞后模型更为广泛;实证分析大多缺乏空间回归模型设定的探讨,Anselin提出三个统计量,并且,如果模型设定正确,应该遵从Wald统计量>Log likelihood统计量>LM统计量的排列顺序。     

Tests for random time effects and spatial error correlation in panel regression models

We consider a panel model with spatial autocorrelation and heterogeneity across time. Various Lagrange multiplier and likelihood ratio test statistics are developed for testing time effects and spatial effects, jointly, marginally or conditionally. Limiting null distributions of the tests are derived. Size and power performances of the proposed tests are compared by a Monte-Carlo experiment.     

云南省少数民族人口分布空间统计分析

空间自相关分析是一种空间统计分析方法,可以反映属性值之间的空间相关性。运用空间统计分析方法对云南省各区县1990年、2002年和2005年少数民族人口分布状况进行分析,发现云南省少数民族人口分布呈现出很强的空间正相关性,少数民族人口分布具有高度稳定性。而少数民族人口增长却表现为与地域无关的非空间相关特性,影响少数民族人口增长的最重要原因是经济因素。     

A general central limit theorem and a subsampling variance estimator for α‐mixing point processes

We establish a central limit theorem for multivariate summary statistics of nonstationary α‐mixing spatial point processes and a subsampling estimator of the covariance matrix of such statistics. The central limit theorem is crucial for establishing asymptotic properties of estimators in statistics for spatial point processes. The covariance matrix subsampling estimator is flexible and model free. It is needed, for example, to construct confidence intervals and ellipsoids based on asymptotic normality of estimators. We also provide a simulation study investigating an application of our results to estimating functions.     

A simulation study on the hybrid nature of Tango's index

Since the early 1990s, there has been an increasing interest in statistical methods for detecting global spatial clustering in data sets. Tango's index is one of the most widely used spatial statistics for assessing whether spatially distributed disease rates are independent or clustered. Interestingly, this statistic can be partitioned into the sum of two terms: one term is similar to the usual chi-square statistic, being based on deviation patterns between the observed and expected values, and the other term, similar to Moran's I, is able to detect the proximity of similar values. In this paper, we examine this hybrid nature of Tango's index. The goal is to evaluate the possibility of distinguishing the spatial sources of clustering: lack of fit or spatial autocorrelation. To comply with the aims of the work, a simulation study is performed, by which examples of patterns driving the goodness-of-fit and spatial autocorrelation components of the statistic are provided. As for the latter aspect, it is worth noting that inducing spatial association among count data without adding lack of fit is not an easy task. In this respect, the overlapping sums method is adopted. The main findings of the simulation experiment are illustrated and a comparison with a previous research on this topic is also highlighted.     

A spatial Bayesian semiparametric mixture model for positive definite matrices with applications in diffusion tensor imaging

Studies on diffusion tensor imaging (DTI) quantify the diffusion of water molecules in a brain voxel using an estimated 3 × 3 symmetric positive definite (p.d.) diffusion tensor matrix. Due to the challenges associated with modelling matrix‐variate responses, the voxel‐level DTI data are usually summarized by univariate quantities, such as fractional anisotropy. This approach leads to evident loss of information. Furthermore, DTI analyses often ignore the spatial association among neighbouring voxels, leading to imprecise estimates. Although the spatial modelling literature is rich, modelling spatially dependent p.d. matrices is challenging. To mitigate these issues, we propose a matrix‐variate Bayesian semiparametric mixture model, where the p.d. matrices are distributed as a mixture of inverse Wishart distributions, with the spatial dependence captured by a Markov model for the mixture component labels. Related Bayesian computing is facilitated by conjugacy results and use of the double Metropolis–Hastings algorithm. Our simulation study shows that the proposed method is more powerful than competing non‐spatial methods. We also apply our method to investigate the effect of cocaine use on brain microstructure. By extending spatial statistics to matrix‐variate data, we contribute to providing a novel and computationally tractable inferential tool for DTI analysis.     

Efficient estimation of nonparametric spatial models with general correlation structures

Spatially correlated data appear in many environmental studies, and consequently there is an increasing demand for estimation methods that take account of spatial correlation and thereby improve the accuracy of estimation. In this paper we propose an iterative nonparametric procedure for modelling spatial data with general correlation structures. The asymptotic normality of the proposed estimators is established under mild conditions. We demonstrate, using both simulation and case studies, that the proposed estimators are more efficient than the traditional locally linear methods which fail to account for spatial correlation.     

Indices of Dependence Between Types in Multivariate Point Patterns

We propose new summary statistics quantifying several forms of dependence between points of different types in a multi-type spatial point pattern. These statistics are the multivariate counterparts of the J -function for point processes of a single type, introduced by Lieshout & Baddeley (1996). They are based on comparing distances from a type i point to either the nearest type j point or to the nearest point in the pattern regardless of type to these distances seen from an arbitrary point in space. Information about the range of interaction can also be inferred. Our statistics can be computed explicitly for a range of well-known multivariate point process models. Some applications to bivariate and trivariate data sets are presented as well.     

Mantel test for spatial functional data

Statistics for spatial functional data is an emerging field in statistics which combines methods of spatial statistics and functional data analysis to model spatially correlated functional data. Checking for spatial autocorrelation is an important step in the statistical analysis of spatial data. Several statistics to achieve this goal have been proposed. The test based on the Mantel statistic is widely known and used in this context. This paper proposes an application of this test to the case of spatial functional data. Although we focus particularly on geostatistical functional data, that is functional data observed in a region with spatial continuity, the test proposed can also be applied with functional data which can be measured on a discrete set of areas of a region (areal functional data) by defining properly the distance between the areas. Based on two simulation studies, we show that the proposed test has a good performance. We illustrate the methodology by applying it to an agronomic data set.