Pedro Macedo

On the Choice of the Ridge Parameter: A Maximum Entropy Approach

In this article, a new method to estimate the ridge parameter, based on the ridge trace and an analytical method borrowed from maximum entropy, is presented. The performance of the new estimator is illustrated through a Monte Carlo simulation study and an empirical application to the well-known Portland cement data set.

Regularization with Maximum Entropy and Quantum Electrodynamics: The Merg(E) Estimators

It is well-known that under fairly conditions linear regression becomes a powerful statistical tool. In practice, however, some of these conditions are usually not satisfied and regression models become ill-posed, implying that the application of traditional estimation methods may lead to non-unique or highly unstable solutions. Addressing this issue, in this paper a new class of maximum entropy estimators suitable for dealing with ill-posed models, namely for the estimation of regression models with small samples sizes affected by collinearity and outliers, is introduced. The performance of the new estimators is illustrated through several simulation studies.

Ridge Regression and Generalized Maximum Entropy: An improved version of the Ridge–GME parameter estimator

ABSTRACT In this article, the Ridge–GME parameter estimator, which combines Ridge Regression and Generalized Maximum Entropy, is improved in order to eliminate the subjectivity in the analysis of the ridge trace. A serious concern with the visual inspection of the ridge trace to define the supports for the parameters in the Ridge–GME parameter estimator is the misinterpretation of some ridge traces, in particular where some of them are very close to the axes. A simulation study and two empirical applications are used to illustrate the performance of the improved estimator. A MATLAB code is provided as supplementary material.

Efficiency in the European agricultural sector: environment and resources

This article intends to compute agriculture technical efficiency scores of 27 European countries during the period 2005–2012, using both data envelopment analysis (DEA) and stochastic frontier analysis (SFA) with a generalized cross-entropy (GCE) approach, for comparison purposes. Afterwards, by using the scores as dependent variable, we apply quantile regressions using a set of possible influencing variables within the agricultural sector able to explain technical efficiency scores. Results allow us to conclude that although DEA and SFA are quite distinguishable methodologies, and despite attained results are different in terms of technical efficiency scores, both are able to identify analogously the worst and better countries. They also suggest that it is important to include resources productivity and subsidies in determining technical efficiency due to its positive and significant exerted influence.

An alternative benchmarking approach for electricity utility regulation using maximum entropy

The main purpose of this study is to present an alternative benchmarking approach that can be used by national regulators of utilities. It is widely known that the lack of sizeable data sets limits the choice of the benchmarking method and the specification of the model to set price controls within incentive-based regulation. Ill-posed frontier models are the problem that some national regulators have been facing. Maximum entropy estimators are useful in the estimation of such ill-posed models, in particular in models exhibiting small sample sizes, collinearity and non-normal errors, as well as in models where the number of parameters to be estimated exceeds the number of observations available. The empirical study involves a sample data used by the Portuguese regulator of the electricity sector to set the parameters for the electricity distribution companies in the regulatory period of 2012-2014. DEA and maximum entropy methods are applied and the efficiency results are compared.

Economic and environmental efficiency in Europe: Evidence from a new stochastic frontier model

This study aims to evaluate the resource and environment efficiency problem of European countries. We specify a new stochastic frontier model where Gross Domestic Product (GDP) is considered as the desirable output and Greenhouse Gases (GHG) emissions as the undesirable output. Capital, Labour, Fossil fuels and Renewable Energy consumption are regarded as inputs. The study is divided into two distinct periods, 2000-2004 and 2005-2011, in order to evaluate the difference between efficiency levels before and after the establishment of environmental targets related with the implementation of the Kyoto Protocol in 2005. A maximum entropy approach to assess technical efficiency is discussed.