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.     

A UNIFYING VIEW ON MULTI‐STEP FORECASTING USING AN AUTOREGRESSION

Abstract This paper unifies two methodologies for multi‐step forecasting from autoregressive time series models. The first is covered in most of the traditional time series literature and it uses short‐horizon forecasts to compute longer‐horizon forecasts, while the estimation method minimizes one‐step‐ahead forecast errors. The second methodology considers direct multi‐step estimation and forecasting. In this paper, we show that both approaches are special (boundary) cases of a technique called partial least squares (PLS) when this technique is applied to an autoregression. We outline this methodology and show how it unifies the other two. We also illustrate the practical relevance of the resultant PLS autoregression for 17 quarterly, seasonally adjusted, industrial production series. Our main findings are that both boundary models can be improved by including factors indicated from the PLS technique.     

Analysis of variance on indirectly measured variables

Abstract  When observations from a normal distribution can only be obtained indirectly by counting the number of subjects responding to a previously chosen dose, parameter estimates can be obtained by using probit analysis. Well-known is the maximum likelihood technique of parameter estimation, less known is the approach by weighted least squares. The latter approach is followed to compare the parameters of several normal distributions by testing their equality, in analogy with the analysis of variance. A practical situation gave rise to this study and it is worked out at the end of the paper.     

Parameter estimation for the drift of a time inhomogeneous jump diffusion process

This work deals with parameter estimation for the drift of jump diffusion processes which are driven by a Lévy process and whose drift term is linear in the parameter. In contrast to the commonly used maximum likelihood estimator, our proposed estimator has the practical advantage that its calculation does not require the evaluation of the continuous part of the sample path. In the important case of an Ornstein‐Uhlenbeck‐type jump diffusion, which is a widely used model, we prove consistency and asymptotic normality.     

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.     

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.     

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.     

An exchange algorithm for computing the least quartile difference estimator

We propose an exchange algorithm (EA) for computing the least quartile difference estimate in a multiple linear regression model. Empirical results suggest that the EA is faster and more accurate than the usual p-subset algorithm.     

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.     

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.     

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。     

耦合Sylvester矩阵方程的梯度迭代算法

通过推广求解矩阵方程AX=b或AX+XB=C的递推迭代算法和基于递阶辩识原理的思想,给出了求解广义耦合矩阵方程的梯度迭代算法。并证明了迭代算法的收敛性。分析表明,若矩阵方程有唯一解,则对任意的初始值该算法给出的迭代解都能快速的收敛到其精确解。数值实例验证了该算法的有效性。