Generalized Cross Entropy Research Articles

The Generalized Cross Entropy Method, with Applications to Probability Density Estimation

Nonparametric density estimation aims to determine the sparsest model that explains a given set of empirical data and which uses as few assumptions as possible. Many of the currently existing methods do not provide a sparse solution to the problem and rely on asymptotic approximations. In this paper we describe a framework for density estimation which uses information-theoretic measures of model complexity with the aim of constructing a sparse density estimator that does not rely on large sample approximations. The effectiveness of the approach is demonstrated through an application to some well-known density estimation test cases.

The distribution of dairy farm size in Poland: a markov approach based on information theory

This article sets out to analyse the evolution of the dairy farm structure of Poland during the post-socialist period. After focusing on how the farm structure has changed over time, an instrumental variable generalized cross entropy estimator is used to develop and estimate a Markov model in order to explore how farm structure will probably develop in the coming decade. The estimator exploits both sample data and prior information, including general and plausible information on farm mobility and structural adjustments based on independent literature. Next, several statistical indicators are computed for farm mobility and for which farms are likely to survive. Finally, milk projections are made and related to policy scenarios. The projections show that the number of dairy farms will continue to decline, but the number of medium and large farms will increase. In the coming decade, subsistence dairy farms are expected to leave the sector slowly. Milk projections show that under the status quo, milk quotas will be binding and overrun, whereas under the 'soft landing' scenario they appear to be only binding after 2010.

Estimating Spatial Autoregressive Models by GME-GCE Techniques

The traditional approach to estimate spatial models bases on a preconceived spatial weights matrix to measure spatial interaction among locations. The a priori assumptions used to define this matrix are supposed to be in line with the ``true'' spatial relationships among the locations of the dataset. Another possibility consists of using some information present on the sample data to specify an empirical matrix of spatial weights. In this article we propose to estimate spatial autoregressive models by generalized maximum entropy (GME) and generalized cross entropy (GCE) econometrics. We compare some traditional methodologies with the proposed GME-GCE estimator by means of Monte Carlo simulations in several scenarios. The results show that the entropy-based estimation techniques can outperform traditional approaches under some circumstances. An empirical case is also studied to illustrate the implementation of the proposed techniques for a real-world example.

A Generalized Cross-Entropy Approach for Modeling Spatially Correlated Counts

This article discusses and applies an information-theoretic framework for incorporating knowledge of the spatial structure in a sample while extracting from it information about processes resulting in count outcomes. The framework, an application of the Generalized Cross-Entropy (GCE) method of estimating count outcome models, allows researchers to incorporate such real-world features as unobserved heterogeneity—with or without spatial clustering—when modeling spatially correlated counts. The information-recovering potential of the approach is investigated using a limited set of simulations. It is then used to study the determinants of counts of homicides recorded in 343 neighborhoods in Chicago, Illinois.

Spatial Spillovers in France: A Study on Individual Count Data at the City Level

Our study aims to measure the effects of spatial R&D spillovers on firms' patent production at the city level. We use an original method to estimate the spatial dimension of spillovers using count data. The method, based on a generalized cross entropy approach, allows us to test spatial auto-correlation. The main result is that when there are local spillovers, their impact on knowledge production is different according to the geographical area and the sector.