线性回归分析的几何学方法

回归分析方法是计量经济学的重要分析方法。传统上的回归分析是用代数等式和矩阵形式表述的。然而从欧氏几何的角度分析回归分析的主要概念、结论,如OLS估计量、被解释变量Y的总平方和分解定理等都有很好的几何直观,可以将许多冗长繁杂的代数公式和推导归结为简单的几何性质。文中给出Frisch-Waugh-Lovell定理的几何解释。     

线性回归模型与传递函数模型在时间序列应用上的比较研究

如果一个因变量是由一个或多个自变量来解释的,那么对这些数据可以建立回归模型.但如果因变量和自变量同时又是时间序列,则也可以建立传递函数模型(transferfunction models).与普通的回归模型相比,传递函数模型说明因变量与自变量以及扰动项之间关系时,有着更为丰富的结构.在多变量时间序列模型方面,有关线性回归模型与传递函数序列在时间序列方面应用效果的比较很少,因此,本文拟进行这方面的研究,为多变量时间序列建立模型提供参考.     

短非平稳时间序列TVAR模型参数PLS估计方法

文章针对短非平稳时间序列TVAR模型的参数估计问题,探讨了一种TVAR模型参数偏最小二乘回归分析方法;通过某飞行器时变机电系统的电压输出序列对本文方法进行了建模实验。实验结果表明:与传统的TVAR模型参数估计方法相比,PLS方法克服了短时间序列所带来的参数估计精度降低的问题,参数辨识精度更高。     

时序模型分析在经济预测中的应用

时间序列分析方法主要就是建立模型,目的是为了描述时间序列中产生数据的随机机制与趋势,以此模型来判断在某一时间或随机机制下会发生的数据达到预测和控制的目的。时间序列可分为平稳的时间序列和非平稳的时间序列,大部分经济时间序列为平稳的时间序列。对于平稳的时间序列进     

国内删失数据统计研究状况综述

研究了国内在线性回归模型、非线性回归模型、半参数回归、非参数回归、单指标回归、生存分析、时间序列分析、密度估计等领域删失数据统计研究状况。     

我国农村居民口粮消费的组合预测

随着农村人口向城镇转移以及农村居民收入的增长,我国农村居民口粮需求逐年下降.预测农村居民口粮消费量不仅有助于把握农村居民消费结构的变动轨迹,而且对指导粮食生产也有重要的意义.文幸针对单一的预测模型可能存在的问题,利用时间序列和线性回归的组合模型对近30年我国农村居民口粮消费量进行了拟合.通过比较单一预测模型和组合预测模型的精度发现:相对于单一的预测模型,组合预测模型预测精度较高.利用组合预测模型,文章预测未来10年我国农村居民的口粮消费量会继续下降.     

基于判定系数和趋势变动的时间序列逐段线性回归

对时间序列进行分割并使用线性回归模型逐段描述,在许多分析中具有重要意义.本文提出了一种新的时间序列分割方法,与基于拟合误差的方法相比,该方法在保证各子序列线性回归模型的拟合优度方面具有明显的优势,而且能够更准确地根据数据的趋势变化进行分割.实证研究也验证了该方法的有效性.     

金融运行异常情况统计监测方法的选择

正从统计学的角度看,金融运行中的异常情况是可以进行界定的。因为在金融运行中我们关心的指标数据一般为时间序列数据,所以金融运行的异常情况在数据上就体现为时间序列数据集中的异常。按照异常的表现形式不同,时间序列的异常主要可以分为点异常和模式异常。这两种异常都可以用于发现一条时间序列或多维时间序列数据集上的     

人口预测的投影寻踪自回归模型构建与实证

文章根据全国和上海市1980—2020年两种完全不同人口变化规律的时间序列数据,采用自回归分析法,确定了3个预测因子,分别建立投影寻踪自回归（PPAR）模型,建模样本的数据拟合精度和验证样本的预测精度均显著高于GM、Logistic模型,完全能够满足人口预测的需要。实证结果表明：全国人口2011—2020年验证样本的平均绝对误差MAE和平均绝对百分比误差MAPE分别为160.0万人和0.116%,最大相对误差仅为0.26%;2021—2030年的人口预测结果表明,2021—2027年,人口增速越来越慢,并于2027年出现人口达峰,达峰人口为14.15亿人。上海市人口2016—2020年验证样本的MAE和MAPE分别为6.9万人和0.28%,最大相对误差仅为0.53%;2021—2027年人口增速越来越慢,并于2027年达峰,达峰人口为2499.9万人。     

基于灰色系统的组合预测模型的建模方法

本文基于灰色系统理论,提出一种非平稳时间序列预测模型的建模方法。该方法首先利用灰色系统模型提取时间序列的趋势项;然后利用样本周期图拟合周期项;最后对去掉趋势项和周期项的序列建立模型,从而完成非平稳时间序列的总体建模。     

Asymptotic Properties of an Estimate of the Prediction Error Variance

An estimate of the variance of the prediction error for a linear stationary time series is constructed by using only a part, ?₀, ?₁,…, ?_M, of the sample autocovariance sequence, where M increases with T, the length of the time series observed. M increases as T^α (α < ¹₄). Under a higher moment condition, but not assuming Gaussianity, the estimate obtained is shown to be strongly consistent and asymptotically normal. The asymptotic variance of the estimation error is also obtained.     

Pooled Cross-Sectional and Time Series Data: A Survey of Current Statistical Methodology

A data base that provides a multivariate statistical history for each of a number of individual entities is called a pooled cross-sectional and time series data base in the econometrics literature. In marketing and survey literature the terms panel data or longitudinal data are often used. In management science a convenient term might be management data base. Such a data base provides a particularly rich environment for statistical analysis. This article reviews methods for estimating multivariate relationships particular to each individual entity and for summarizing these relationships for a number of individuals. Inference to a larger population when the data base is viewed as a sample is also considered.     

《九章算术》中的统计学思想探究

《九章算术》是中国历史上最著名的一部数学经典,该书以应用问题求解的形式为成书体例,而这些问题基本都与社会经济有关,因此书中蕴涵了丰富的统计学思想。本文从统计范围和统计思想的角度对书中的统计知识进行了分析,探讨了书中诸如统计分组、抽样推断、线性回归分析及比例关系等统计理论,并据此对当时中国古代统计思想的发展状况进行了研究。     

Statistical Control for Road Pavements

Roads are assets vital to the economies of nations, particularly those with such low population density as Australia and New Zealand. The quality of road construction is of great importance. The application of statistical techniques to determining whether the construction of road pavement is being carried out to the design specification can be of great benefit to administrators and contractors. In this paper, a method is presented for obtaining control limits for a means chart when correlated observations are taken over a grid on a two‐dimensional surface. Data from a closely monitored road construction project are used to determine if the construction process can be considered ‘in control’. The nature of the correlation structure is determined using ARIMA models. The ultimate aim of the control charts and specifications is to control base course thickness. Controlling the pavement surfaces is a means to this end.     

Improved local polynomial estimation in time series regression

We propose a modification of local polynomial estimation which improves the efficiency of the conventional method when the observation errors are correlated. The procedure is based on a pre-transformation of the data as a generalization of the pre-whitening procedure introduced by Xiao et al. [(2003), ‘More Efficient Local Polynomial Estimation in Nonparametric Regression with Autocorrelated Errors’, Journal of the American Statistical Association, 98, 980–992]. While these authors assumed a linear process representation for the error process, we avoid any structural assumption. We further allow the regressors and the errors to be dependent. More importantly, we show that the inclusion of both leading and lagged variables in the approximation of the error terms outperforms the best approximation based on lagged variables only. Establishing its asymptotic distribution, we show that the proposed estimator is more efficient than the standard local polynomial estimator. As a by-product we prove a suitable version of a central limit theorem which allows us to improve the asymptotic normality result for local polynomial estimators by Masry and Fan [(1997), ‘Local Polynomial Estimation of Regression Functions for Mixing Processes’, Scandinavian Journal of Statistics, 24, 165–179]. A simulation study confirms the efficiency of our estimator on finite samples. An application to climate data also shows that our new method leads to an estimator with decreased variability.     

A diagnostic statistic for functional-coefficient autoregressive models

In this paper, functional coefficient autoregressive (FAR) models proposed by Chen and Tsay (1993) are considered. We propose a diagnostic statistic for FAR models constructed by comparing between parametric and nonparametric estimators of the functional form of the FAR models. We show asymptotic properties of our statistic mathematically and it can be applied to the estimation of the delay parameter and the specification of the functional form of FAR models.     

Statistical Inference in Orthogonal Regression for Three-Part Compositional Data Using a Linear Model with Type-II Constraints

Orthogonal regression is a proper tool to analyze relations between two variables when three-part compositional data, i.e., three-part observations carrying relative information (like proportions or percentages), are under examination. When linear statistical models with type-II constraints (constraints involving other parameters besides the ones of the unknown model) are employed for estimating the parameters of the regression line, approximate variances and covariances of the estimated line coefficients can be determined. Moreover, the additional assumption of normality enables to construct confidence domains and perform hypotheses testing. The theoretical results are applied to a real-world example.     

On the Smoothness of Projections in Statistical Models

Here we examine the existence of the projection of a probability measure in a parametric statistical model. Once, in a general framework, the existence of the projection is established, we consider the problem from a statistical point of view, modeling a parametric statistical model as a convenient manifold.     

Subsampling the Gibbs Sampler

This article provides a justification of the ban against sub-sampling the output of a stationary Markov chain that is suitable for presentation in undergraduate and beginning graduate-level courses. The justification does not rely on reversibility of the chain as does Geyer's (1992) argument and so applies to the usual implementation of the Gibbs sampler.     

Predicting hospital census using time series regression methods

We first describe the time series modeling problem in a general way. Then some specific assumptions and observations which are pertinent to the application of these models are made. We next propose a specific approach to the modeling problem, one which yields efficient, easily calculated estimators of all parameters (under the stated assumptions). Finally, the technique is applied to the problem of modeling the census of a particular hospital.