Using Weighted Least Squares to Deflate Input–Output Tables

This article proposes a balancing procedure for the deflation of input–output (I-O) tables from the viewpoint of users. This is a ‘subjective’ variant of the Weighted Least Squares (WLS) method, already known in the literature. It is argued that it is more flexible than other methods, and it is shown that SWLS subsumes the first-order approximation of RAS as a special case. Flexibility is due to the facts that (a) users can attach differential ‘reliability’ weights to first (unbalanced) estimates, depending on the confidence they have in the different parts of their pre-balancing work, (b) differently from RAS, one is not bound to take any row or column total as exogenously given, and (c) additional constraints can be added to it. The article describes also how SWLS was utilised to estimate a yearly (1959–2000) series of constant-price I-O tables for the Italian economy.     

MSE-improvement of the least squares estimator by dropping variables

It is well known that dropping variables in regression analysis decreases the variance of the least squares (LS) estimator of the remaining parameters. However, after elimination estimates of these parameters are biased, if the full model is correct. In his recent paper, Boscher (1991) showed that the LS-estimator in the special case of a mean shift model (cf. Cook and Weisberg, 1982) which assumes no “outliers” can be considered in the framework of a linear regression model where some variables are deleted. He derived conditions under which this estimator outperforms the LS-estimator of the full model in terms of the mean squared error (MSE)-matrix criterion. We demonstrate that this approach can be extended to the general set-up of dropping variables. Necessary and sufficient conditions for the MSE-matrix superiority of the LS-estimator in the reduced model over that in the full model are derived. We also provide a uniformly most powerful F-statistic for testing the MSE-improvement.     

Polytomous logistic regression

In this paper a review will be given of some methods available for modelling relationships between categorical response variables and explanatory variables. These methods are all classed under the name polytomous logistic regression (PLR). Models for PLR will be presented and compared; model parameters will be tested and estimated by weighted least squares and by likelihood. Usually, software is needed for computation, and available statistical software is reported.
An industrial problem is solved to some extent as an example to illustrate the use of PLR. The paper is concluded by a discussion on the various PLR-methods and some topics that need a further study are mentioned.     

Efficiency of iterated WLS in the linear model with completely unknown heteroskedasticity

Iterated weighted least squares (IWLS) is investigated for estimating the regression coefficients in a linear model with symmetrically distributed errors. The variances of the errors are not specified; it is not assumed that they are unknown functions of the explanatory variables nor that they are given in some parametric way.
IWLS is carried out in a random number of steps, of which the first one is OLS. In each step the error variance at time t is estimated with a weighted sum of m squared residuals in the neighbourhood of t and the coefficients are estimated using WLS. Furthermore an estimate of the co-variance matrix is obtained. If this estimate is minimal in some way the iteration process is stopped.
Asymptotic properties of IWLS are derived for increasing sample size n . Some particular cases show that the asymptotic efficiency can be increased by allowing more than two steps. Even asymptotic efficiency with respect to WLS with the true error variances can be obtained if m is not fixed but tends to infinity with n and if the heteroskedasticity is smooth.     

Analysis of Categorical Data for Complex Surveys

This paper reviews methods for handling complex sampling schemes when analysing categorical survey data. It is generally assumed that the complex sampling scheme does not affect the specification of the parameters of interest, only the methodology for making inference about these parameters. The organisation of the paper is loosely chronological. Contingency table data are emphasised first before moving on to the analysis of unit‐level data. Weighted least squares methods, introduced in the mid 1970s along with methods for two‐way tables, receive early attention. They are followed by more general methods based on maximum likelihood, particularly pseudo maximum likelihood estimation. Point estimation methods typically involve the use of survey weights in some way. Variance estimation methods are described in broad terms. There is a particular emphasis on methods of testing. The main modelling methods considered are log‐linear models, logit models, generalised linear models and latent variable models. There is no coverage of multilevel models.     

关于我国城镇最佳规模的实证检验

关于城镇最佳规模问题,在我国学术界和政府部门一直存在争议.通过对相关理论分歧的归纳和西方学者关于最佳城镇规模研究的梳理,借鉴英国学者巴顿(K.J.Buton)的理论,运用我国的城市统计资料构建计量模型,分别从行政管理角度最佳、市民角度最佳和企业生产角度最佳三个方面,实证检验了我国最佳的城镇人口规模.相关结论对于正确选择我国的城市化道路,推动政府部门合理规划城市发展,具有一定的参考价值.     

An application of approximate finite sample results to parameter estimation in a linear errors-in-variables model

In the simple errors-in-variables model the least squares estimator of the slope coefficient is known to be biased towards zero for finite sample size as well as asymptotically. In this paper we suggest a new corrected least squares estimator, where the bias correction is based on approximating the finite sample bias by a lower bound. This estimator is computationally very simple. It is compared with previously proposed corrected least squares estimators, where the correction aims at removing the asymptotic bias or the exact finite sample bias. For each type of corrected least squares estimators we consider the theoretical form, which depends on an unknown parameter, as well as various feasible forms. An analytical comparison of the theoretical estimators is complemented by a Monte Carlo study evaluating the performance of the feasible estimators. The new estimator proposed in this paper proves to be superior with respect to the mean squared error.     

The analysis of proportions in agricultural experiments by a generalized linear mixed model

This paper is concerned with the statistical analysis of proportions involving extra-binomial variation. Extra-binomial variation is inherent to experimental situations where experimental units are subject to some source of variation, e.g. biological or environmental variation. A generalized linear model for proportions does not account for random variation between experimental units. In this paper an extended version of the generalized linear model is discussed with special reference to experiments in agricultural research. In this model it is assumed that both treatment effects and random contributions of plots are part of the linear predictor. The methods are applied to results from two agricultural experiments.     

Testing for equality of variance of correlated normal variables

A standard test exists for whether bivariate normal data of arbitrary correlation have equal variances. An extension of this model is useful to test whether two measuring instruments, with which repeated measurements have been made on each of n units, have equal error variance. It is shown that one or two simple F -distributed statistics yield performance comparable with that of the generalized likelihood ratio statistic.     

A minimum chi-squared method for indirect parameter estimation from Poisson data

In this paper, we introduce a new algorithm for estimating non-negative parameters from Poisson observations of a linear transformation of the parameters. The proposed objective function fits both a weighted least squares (WLS) and a minimum χ² estimation framework, and results in a convex optimization problem. Unlike conventional WLS methods, the weights do not need to be estimated from the datas, but are incorporated in the objective function. The iterative algorithm is derived from an alternating projection procedure in which "distance" is determined by the chi-squared test statistic, which is interpreted as a measure of the discrepancy between two distributions. This may be viewed as an alternative to the Kullback-Leibler divergence which corresponds to the maximum likelihood (ML) estimation. The algorithm is similar in form to, and shares many properties with, the expectation maximization algorithm for ML estimation. In particular, we show that every limit point of the algorithm is an estimator, and the sequence of projected (by the linear transformation into the data space) means converge. Despite the similarities, we show that the new estimators are quite distinct from ML estimators, and obtain conditions under which they are identical.     

Optimal versus orthogonal and equivalent-estimation design of blocked and split-plot experiments

This article provides an overview of the recent literature on the design of blocked and split-plot experiments with quantitative experimental variables. A detailed literature study introduces the ongoing debate between an optimal design approach to constructing blocked and split-plot designs and approaches where the equivalence of ordinary least squares and generalized least squares estimates are envisaged. Examples where the competing design strategies lead to totally different designs are given, as well as examples in which the optimal experimental designs are orthogonally blocked or equivalent-estimation split-plot designs.     

基于偏最小二乘的泰国菠萝出口影响因素实证研究

本文采用偏最小二乘回归模型(PLS),以泰国菠萝贸易为例,通过变量投影重要性准则筛选自变量,由交叉有效性提取主成分,进而建立偏最小二乘回归模型。深入分析了各指标对泰国菠萝出口贸易的影响。研究表明泰国菠萝出口与原料价格及工厂生产加工速度密切相关,并且偏最小二乘回归的拟合效果优于普通最小二乘回归。     

Partial Minimax Estimation in Regression Analysis

The general minimax estimator of the linear regression model is applicable when the whole parameter vector is restricted to an ellipsoid. In many applications, however, it is more realistic to assume that only a part of the parameter set is constrained. For this case an alternative minimax approach is developed.     

Re-examining 50-year-old OLS estimates of the Klein–Goldberger model

This paper examines the ordinary least squares estimates of the Klein–Goldberger model by Fox ( Journal of Political Economy , 64 , 1956, 128). Because Klein and Goldberger published the data set with the model, it is possible to re-examine Fox's results years later, and investigate the accuracy with which these estimates were calculated. The examination reported in this paper was conducted by making independent estimates using three different modern econometric software packages. This examination reveals that the Fox estimates for a number of the equations of this model are replicable, to the two or three digits reported by Fox. Fox's results for other equations cannot be replicated. Not all the reasons for this lack of replicability can be determined, but in several cases the computational methods used by Fox and his assistants have been found to be faulty by modern computational standards.     

区域物流通道容量预测研究

将偏最小二乘回归模型与灰色GM(1,1)校正模型进行有机结合,建立组合预测模型,取得了令人满意的预测精度,为区域物流通道容量预测提供了一种新的思路和方法。     

基于拟牛顿法频率域全波形反演研究

全波形反演是综合利用地震波场的运动学和动力学参数,通过最小二乘来拟合实际波场和预测波场,从而获得地质结构和岩性资料的方法。本文先简述了频率域地震波正演,之后利用拟牛顿法来推导频率域全波形反演,克服了高斯——牛顿法中海森矩阵可能奇异或者非正定特性,通过图形对比,得到频率域全波形反演局限在于频率的缺失和来自其它地质结构对三维地质模型受到的影响比较大,合理选择频点和频宽进行反演可解决频率缺失的影响,二维地质模型的反演效果理想,而三维地质模型的反演有待提高和改进。     

2SLS and OLS in a spatial autoregressive model with equal spatial weights

The paper considers a Cliff–Ord type spatial model with a spatially lagged dependent variable and a row normalized weighting matrix with equal weights. We show that the 2SLS and OLS estimators are inconsistent unless panel data are available. The weighting matrix in question is one which would naturally be considered if all units are neighbors to each other, and there is no other reasonable or observable measure of distance between them.     

Pitfalls of Normal-Gamma Stochastic Frontier Models

Although conceptually pleasing, normal-gamma frontier models lead to difficult estimation problems. It is shown here that unless the sample size reaches several thousands of observations the shape parameter of the gamma density is hard to estimate, and that this carries over to estimates of the stochastic frontier, the individual inefficiencies, and the allocation of the overall variance to the stochastic frontier and to the inefficiencies.     

Combining Modelling Strategies to Analyse Teaching Styles Data

This paper combines two estimation procedures: Iterative Generalized Least Squares as used in the software MLwiN; Gibbs Sampling as employed in thesoftware BUGS to produce a modelling strategy that respects the hierarchical natureof the Teaching Styles data and also allows for the endogeneity problems encountered when examining pupil progress.