SENSITIVITY OF THE GME ESTIMATES TO SUPPORT BOUNDS

The claim has been made that the Generalized Maximum Entropy (GME) estimator of Golan, Judge and Miller is not sensitive to variations in the support bounds of either the parameters or the error terms. In this paper, we scrutinized this claim by means of Monte Carlo experiments and found that the parameter estimates are impacted in a substantial way by these changes. We also analyzed the famous data sample on the US manufacturing industry used by Cobb and Douglas in 1934 and found that the GME estimator is very sensitive to changes in support bounds. We conclude with a general result by Caputo and Paris according to which any support bound variation produces unexpected responses in the parameter estimates.Research Methods/ Statistical Methods,

MELE: MAXIMUM ENTROPY LEUVEN ESTIMATORS

Multicollinearity hampers empirical econometrics. The remedies proposed to date suffer from pitfalls of their own. The ridge estimator is not generally accepted as a vital alternative to the ordinary least-squares (OLS) estimator because it depends upon unknown parameters. The generalized maximum entropy (GME) estimator of Golan, Judge and Miller depends upon subjective exogenous information that affects the estimated parameters in an unpredictable way. This paper presents novel maximum entropy estimators inspired by the theory of light that do not depend upon any additional information. Monte Carlo experiments show that they are not affected by any level of multicollinearity and dominate OLS uniformly. The Leuven estimators are consistent and asymptotically normal.multicollinearity, mean squared error, ordinary least squares, generalized maximum entropy, Research Methods/ Statistical Methods, C2,

ECONOMIC RESEARCH OF INTEREST TO AGRICULTURE, 1997-1999

This bibliography of Giannini Foundation members' publications, Economic Research of Interest to Agriculture was first issued on May 6, 1951, the eighty-first birthday of A.P. Giannini, and included the Giannini Foundation of Agricultural Economics members' works from 1929 through 1950. The first three issues were compiled and edited by the Giannini Foundation's first librarian, Orpha E. Cummings, 1930-1958. The issues that followed were edited by librarians, Mary Lida Eakin, 1958-1967; Virginia A. Fox, 1967-1980; and Grace Dote, 1970-2001.Teaching/Communication/Extension/Profession,

Evaluation of estimators for ill-posed statistical problems subject to multicollinearity

Multicollinearity is a significant problem in economic analysis and occurs in any situation where at least two of the explanatory variables in a model are related to one another. The presence of multicollinearity is problematic, as changes in the dependent variable cannot be accurately attributed to individual explanatory variables. It can cause estimated coefficients to be unstable and have high variances, and thus be potentially inaccurate and inappropriate to guide management or policy. Due to this problem, many alternative estimators have been developed for the analysis of multicollinear data. The primary objective of this thesis is to compare and contrast the performance of some of these common estimators, as well as a number of new estimators, and test their prediction accuracy and precision under various circumstances. Through the use of non-trivial Monte Carlo experiments, the estimators are tested under 10 different levels of multicollinearity, with regressors and errors drawn from different distributions (normal, student t, chi-squared, and in the case of errors, mixed Gaussian). Insights are gained through response surface analysis, which is conducted to help summarise the output of these simulations. A number of key findings are identified. The highest levels of mean square error (MSE) are generally given by a Generalised Maximum Entropy estimator with narrow support bounds defined for its coefficients (GMEN) and the One-Step Data Driven Entropy (DDE1) model. Yet, none of the estimators evaluated produced sufficiently high levels of MSE to suggest that they were inappropriate for prediction. The most accurate predictions, regardless of the distributions tested or multicollinearity, were given by Ordinary Least Squares (OLS). The Leuven-2 estimator appeared relatively robust in terms of MSE, being reasonably invariant to changes in condition number, and error distribution. However, it was unstable due to variability in error estimation arising from the arbitrary way that probabilities are converted to coefficient values in this framework. In comparison, MSE values for Leuven-1 were low and far more stable than those reported for Leuven-2. The estimators that produced the least precision risk, as measured through mean square error loss (MSEL), were the GMEN and Leuven-1 estimators. However, the GMEN model requires exogenous information and, as such, is much more problematic to accurately apply in different contexts. In contrast, two models had very poor precision in the presence of multicollinear data, the Two-Step Data Driven Entropy (DDE2) model and OLS, rendering them inappropriate for estimation in such circumstances. Overall, these results highlight that the Leuven-1 estimator is the most appropriate if a practitioner wishes to achieve high prediction accuracy and precision in the presence of multicollinearity. Nevertheless, it is critical that more attention is paid to the theoretical basis of the Leuven-1 estimator, as relating estimated probabilities to coefficients using concepts drawn from the theory of light appears highly subjective. This is illustrated through the differences in empirical results obtained for the Leuven-1 and Leuven-2 estimators

Comparative Statics Of The Generalized Maximum Entropy Estimator Of The General Linear Model

The generalized maximum entropy method of information recovery requires that an analyst provides prior information in the form of finite bounds on the permissible values of the regression coefficients and error values for its implementation. Using a new development in the method of comparative statics, the sensitivity of the resulting coefficient and error estimates to the prior information is investigated. A negative semidefinite matrix reminiscent of the Slutsky-matrix of neoclassical microeconomic theory is shown to characterize the said sensitivity, and an upper bound for the rank of the matrix is derived. © 2007 Elsevier B.V. All rights reserved

Comparative statics of the generalized maximum entropy estimator of the general linear model

The generalized maximum entropy method of information recovery requires that an analyst provides prior information in the form of finite bounds on the permissible values of the regression coefficients and error values for its implementation. Using a new development in the method of comparative statics, the sensitivity of the resulting coefficient and error estimates to the prior information is investigated. A negative semidefinite matrix reminiscent of the Slutsky-matrix of neoclassical microeconomic theory is shown to characterize the said sensitivity, and an upper bound for the rank of the matrix is derived. (c) 2007 Elsevier B.V. All rights reserved

Contributos para a teoria de máxima entropia na estimação de modelos mal-postos

Doutoramento em MatemáticaAs técnicas estatísticas são fundamentais em ciência e a análise de regressão linear é, quiçá, uma das metodologias mais usadas. É bem conhecido da literatura que, sob determinadas condições, a regressão linear é uma ferramenta estatística poderosíssima. Infelizmente, na prática, algumas dessas condições raramente são satisfeitas e os modelos de regressão tornam-se mal-postos, inviabilizando, assim, a aplicação dos tradicionais métodos de estimação. Este trabalho apresenta algumas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, em particular na estimação de modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. A investigação é desenvolvida em três vertentes, nomeadamente na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, na estimação do parâmetro ridge em regressão ridge e, por último, em novos desenvolvimentos na estimação com máxima entropia. Na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, o trabalho desenvolvido evidencia um melhor desempenho dos estimadores de máxima entropia em relação ao estimador de máxima verosimilhança. Este bom desempenho é notório em modelos com poucas observações por estado e em modelos com um grande número de estados, os quais são comummente afetados por colinearidade. Espera-se que a utilização de estimadores de máxima entropia contribua para o tão desejado aumento de trabalho empírico com estas fronteiras de produção. Em regressão ridge o maior desafio é a estimação do parâmetro ridge. Embora existam inúmeros procedimentos disponíveis na literatura, a verdade é que não existe nenhum que supere todos os outros. Neste trabalho é proposto um novo estimador do parâmetro ridge, que combina a análise do traço ridge e a estimação com máxima entropia. Os resultados obtidos nos estudos de simulação sugerem que este novo estimador é um dos melhores procedimentos existentes na literatura para a estimação do parâmetro ridge. O estimador de máxima entropia de Leuven é baseado no método dos mínimos quadrados, na entropia de Shannon e em conceitos da eletrodinâmica quântica. Este estimador suplanta a principal crítica apontada ao estimador de máxima entropia generalizada, uma vez que prescinde dos suportes para os parâmetros e erros do modelo de regressão. Neste trabalho são apresentadas novas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, tendo por base o estimador de máxima entropia de Leuven, a teoria da informação e a regressão robusta. Os estimadores desenvolvidos revelam um bom desempenho em modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. Por último, são apresentados alguns códigos computacionais para estimação com máxima entropia, contribuindo, deste modo, para um aumento dos escassos recursos computacionais atualmente disponíveis.Statistical techniques are essential in most areas of science being linear regression one of the most widely used. It is well-known that under fairly conditions linear regression is a powerful statistical tool. Unfortunately, some of these conditions are usually not satisfied in practice and the regression models become ill-posed, which means that the application of traditional estimation methods may lead to non-unique or highly unstable solutions. This work is mainly focused on the maximum entropy estimation of ill-posed models, in particular the estimation of regression models with small samples sizes affected by collinearity and outliers. The research is developed in three directions, namely the estimation of technical efficiency with state-contingent production frontiers, the estimation of the ridge parameter in ridge regression, and some developments in maximum entropy estimation. In the estimation of technical efficiency with state-contingent production frontiers, this work reveals that the maximum entropy estimators outperform the maximum likelihood estimator in most of the cases analyzed, namely in models with few observations in some states of nature and models with a large number of states of nature, which usually represent models affected by collinearity. The maximum entropy estimators are expected to make an important contribution to the increase of empirical work with state-contingent production frontiers. The main challenge in ridge regression is the selection of the ridge parameter. There is a huge number of methods to estimate the ridge parameter and no single method emerges in the literature as the best overall. In this work, a new method to select the ridge parameter in ridge regression is presented. The simulation study reveals that, in the case of regression models with small samples sizes affected by collinearity, the new estimator is probably one of the best ridge parameter estimators available in the literature on ridge regression. Founded on the Shannon entropy, the ordinary least squares estimator and some concepts from quantum electrodynamics, the maximum entropy Leuven estimator overcomes the main weakness of the generalized maximum entropy estimator, avoiding exogenous information that is usually not available. Based on the maximum entropy Leuven estimator, information theory and robust regression, new developments on the theory of maximum entropy estimation are provided in this work. The simulation studies and the empirical applications reveal that the new estimators are a good choice in the estimation of linear regression models with small samples sizes affected by collinearity and outliers. Finally, a contribution to the increase of computational resources on the maximum entropy estimation is also accomplished in this work