On LSE in regression model for long-range dependent random fields on spheres

We study the asymptotic behaviour of least squares estimators (LSE) in regression models for long-range dependent random fields observed on spheres. The LSE can be given as a weighted functional of long-range dependent random fields. It is known that in this scenario the limits can be non-Gaussian. We derive the limit distribution and the corresponding rate of convergence for the estimators. The results were obtained under rather general assumptions on the random fields. Simulation studies were conducted to support theoretical findings.     

A Simulation Study of Some Ridge Regression Estimators under Different Distributional Assumptions

Based on the work of Khalaf and Shukur (2005 Khalaf , G. , Shukur , G. ( 2005 ). Choosing ridge parameters for regression problems . Communications in Statistics – Theory and Methods 34 : 1177 – 1182 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Alkhamisi et al. (2006 Alkhamisi , M. , Khalaf , G. , Shukur , G. ( 2006 ). Some modifications for choosing ridge parameters . Communications in Statistics – Theory and Methods 35 : 2005 – 2020 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and Muniz et al. (2010 Muniz , G. , Kibria , B. M. G. , Shukur , G. ( 2010 ). On developing ridge regression parameters: a graphical Investigation. Submitted for Publication . [Google Scholar]), this article considers several estimators for estimating the ridge parameter k. This article differs from aforementioned articles in three ways: (1) Data are generated from Normal, Student's t, and F distributions with appropriate degrees of freedom; (2) The number of regressors considered are from 4–12 instead of 2–4, which are the usual practice; (3) Both mean square error (MSE) and prediction sum of square (PRESS) are considered as the performance criterion. A simulation study has been conducted to compare the performance of the estimators. Based on the simulation study we found that, increasing the correlation between the independent variables has negative effect on the MSE and PRESS. However, increasing the number of regressors has positive effect on MSE and PRESS. When the sample size increases the MSE decreases even when the correlation between the independent variables is large. It is interesting to note that the dominance pictures of the estimators are remained the same under both the MSE and PRESS criterion. However, the performance of the estimators depends on the choice of the assumption of the error distribution of the regression model.     

A Summary of Some Research on PC and Bayesian PC Criterion in China

In the past two decades, Pitman closeness (PC) criterion has been studied intensively in China. But many of research works were written in Chinese, which cannot be accessed by researchers from other countries. In this paper, we briefly summarize part of main results on the PC criterion in linear model in China. First, we present the basic model and some definitions. Then, we introduce the PC superiority for covariance adjustment estimate, and a class of biased estimates such as a kind of linear estimate, James–Stein estimate and the principal components estimate. Third, we introduce Bayesian PC superiorities for several different linear models such as ordinary univariate regression model, multivariate linear model and analysis of variance model. Finally, some results of robustness under Bayesian PC criterion are shown.     

Performance of some ridge regression estimators for the multinomial logit model

This article considers several estimators for estimating the ridge parameter k for multinomial logit model based on the work of Khalaf and Shukur (2005 Khalaf, G., and G. Shukur. 2005. Choosing ridge parameters for regression problems. Commun. Statist. Theor. Meth., 34:1177–1182.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), Alkhamisi et al. (2006 Alkhamisi, M., G. Khalaf, and G. Shukur. 2006. Some modifications for choosing ridge parameters. Commun. Statist. Theor. Meth. 35:2005–2020.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), and Muniz et al. (2012 Muniz, G., B. M. G. Kibria, K. Månsson, and G. Shukur. 2012. On developing ridge regression parameters: A graphical investigation. in SORT. 36: 115–138.[Web of Science ®] , [Google Scholar]). The mean square error (MSE) is considered as the performance criterion. A simulation study has been conducted to compare the performance of the estimators. Based on the simulation study we found that increasing the correlation between the independent variables and the number of regressors has negative effect on the MSE. However, when the sample size increases the MSE decreases even when the correlation between the independent variables is large. Based on the minimum MSE criterion some useful estimators for estimating the ridge parameter k are recommended for the practitioners.     

Hayek and the Methodenstreit at the LSE

ABSTRACT

Friedrich Hayek’s Inaugural Address at the London School of Economics (LSE), ‘The Trend of Economic Thinking’ (1 March 1933), has been recognized as of particular importance for the understanding of his work. In it, Hayek argues that economics has a key role of showing what we cannot achieve: of showing that some attractive ideals are utopian. In developing this theme, Hayek referred to Mises’ arguments about the problems of economic calculation under socialism; but the idea – which I suggest might be seen as a theory about the structural constraints imposed by a flourishing market economy – becomes a more general motif in Hayek’s work. In the lecture, Hayek’s ideas are developed through engagement with the younger German Historical School of economics, which is criticized for espousing methodological ideas that would call the idea of such constraints into question. In this article, I suggest that there were also local targets at the LSE. I discuss the way in which William Beveridge, the Director of the LSE, and Lancelot Hogben, who held a Chair in Social Biology there, were engaged in an extended empiricist critique of the methodological ideas of the LSE economists and of theoretical economists more generally in ways close to the younger German historical school.     

Multivariate portmanteau test for structural VARMA models with uncorrelated but non-independent error terms

We consider portmanteau tests for testing the adequacy of structural vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. The structural forms are mainly used in econometrics to introduce instantaneous relationships between economic variables. We first study the joint distribution of the quasi-maximum likelihood estimator (QMLE) and the noise empirical autocovariances. We then derive the asymptotic distribution of residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We deduce the asymptotic distribution of the Ljung-Box (or Box-Pierce) portmanteau statistics in this framework. It is shown that the asymptotic distribution of the portmanteau tests is that of a weighted sum of independent chi-squared random variables, which can be quite different from the usual chi-squared approximation used under independent and identically distributed (iid) assumptions on the noise. Hence we propose a method to adjust the critical values of the portmanteau tests. Monte Carlo experiments illustrate the finite sample performance of the modified portmanteau test.     

生长曲线最小二乘估计和最佳线性无偏估计相等的几个充要条件

讨论了生长曲线未知参数的最小二乘估计与最佳线性无偏估计相等的几个充要条件,并给出了主要结论的两种不同证明。