SABIIA - Sistema Aberto e Integrado de Informação em Agricultura (Sabiia)

In the Empirical Estimating Equations (E^3) approach to estimation and inference estimating equations are replaced by their data-dependent empirical counterparts. It is odd but with E^3 there are models where the E^3-based estimator does not exist for some data set, and does exist for others. This depends on whether or not a set of data-supported probability mass functions that satisfy the empirical estimating equations is empty for the data set. In a finite sample context, this unnoted feature invalidates methods of estimation and inference, such as the Maximum Empirical Likelihood, that operate within E^3. The empty set problem of E^3 is illustrated by several examples and possible remedies are discussed.

Large Deviations Theory and Empirical Estimator Choice

Palavras-chave: Statistical theory; Statistics; Mathematical analysis; Mathematical statistic; Research Methods/ Statistical Methods.

Ano: 2009

URL: http://purl.umn.edu/53402

Criterion choice is such a hard problem in information recovery and in estimation and inference. In the case of inverse problems with noise, can probabilistic laws provide a basis for empirical estimator choice? That is the problem we investigate in this paper. Large Deviations Theory is used to evaluate the choice of estimator in the case of two fundamental situations-problems in modelling data. The probabilistic laws developed demonstrate that each problem has a unique solution-empirical estimator. Whether other members of the empirical estimator family can be associated a particular problem and conditional limit theorem, is an open question.

Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods

Palavras-chave: Research Methods/ Statistical Methods.

Ano: 2006

URL: http://purl.umn.edu/25084

Mittelhammer, Ronald C.; Judge, George G.; Schoenberg, Ron.

This paper presents empirical evidence concerning the finite sample performance of conventional and generalized empirical likelihood-type estimators that utilize instruments in the context of linear structural models characterized by endogenous explanatory variables. There are suggestions in the literature that traditional and non-traditional asymptotically efficient estimators based on moment equations may, for the relatively small sample sizes usually encountered in econometric practice, have relatively large biases and/or variances and provide an inadequate basis for estimation and inference. Given this uncertainty we use a range of data sampling processes and Monte Carlo sampling procedures to accumulate finite sample empirical evidence concerning...

Minimum Divergence Moment Based Binary Response Models: Estimation and Inference

Palavras-chave: Unbiased moment based estimation and inference; Empirical likelihood; Empirical exponential likelihood; Semiparametric models; Conditional estimating equations; Finite sample bias and precision; Squared error loss; Instrumental conditioning variables; Research Methods/ Statistical Methods; C10; C24.

Ano: 2003

URL: http://purl.umn.edu/25090

Mittelhammer, Ronald C.; Judge, George G.; Miller, Douglas J.; Cardell, N. Scott.

This paper introduces a new class of estimators based on minimization of the Cressie-Read (CR) power divergence measure for binary choice models, where neither a parameterized distribution nor a parameterization of the mean is specified explicitly in the statistical model. By incorporating sample information in the form of conditional moment conditions and estimating choice probabilities by optimizing a member of the set of divergence measures in the CR family, a new class of nonparametric estimators evolves that requires less a priori model structure than conventional parametric estimators such as probit or logit. Asymptotic properties are derived under general regularity conditions and finite sampling properties are illustrated by Monte Carlo sampling...

Estimation and Statistical Inference in Economics

Palavras-chave: Nonparametric binary response models and estimators; Conditional moment equations; Finite sample bias and precision; Squared error loss; Response variables; Cressie-Read statistic; Information theoretic methods; Research Methods/ Statistical Methods; C10; C2.

Ano: 2005

URL: http://purl.umn.edu/25020

Estimating the Link Function in Multinomial Response Models under Endogeneity and Quadratic Loss

Judge, George G..

Tipo: Book

Palavras-chave: Research Methods/ Statistical Methods.

Ano: 1977

URL: http://purl.umn.edu/95543

Judge, George G.; Mittelhammer, Ronald C..

This paper considers estimation and inference for the multinomial response model in the case where endogenous variables are arguments of the unknown link function. Semiparametric estimators are proposed that avoid the parametric assumptions underlying the likelihood approach as well as the loss of precision when using nonparametric estimation. A data based shrinkage estimator that seeks an optimal combination of estimators and results in superior risk performance under quadratic loss is also developed.

The information theoretic foundations of a probabilistic and predictive micro and macro economics

Palavras-chave: Multinomial Process; Endogeneity; Empirical likelihood procedures; Quadratic loss; Semiparametric estimation and inference; Data dependent shrinkage; Asymptotic and finite sample risk; Research Methods/ Statistical Methods; C10; C24.

Ano: 2004

URL: http://purl.umn.edu/25095

Consistency of Empirical Likelihood and Maximum A-Posteriori Probability Under Misspecification

Judge, George G..

Despite the productive efforts of economists, the disequilibrium nature of the economic system and imprecise predictions persist. One reason for this outcome is that traditional econometric models and estimation and inference methods cannot provide the necessary quantitative information for the causal influence-dynamic micro and macro questions we need to ask given the noisy indirect effects data we use. To move economics in the direction of a probabilistic and causal based predictive science, in this paper information theoretic estimation and inference methods are suggested as a basis for understanding and making predictions about dynamic micro and macro economic processes and systems.

Tipo: Working Paper

Palavras-chave: Information theoretic methods; State space models; First order Markov processes; Inverse problems; Dynamic economic systems; Research Methods/ Statistical Methods; C40; C51.

Ano: 2012

URL: http://purl.umn.edu/122890

Using a large deviations approach, Maximum A-Posteriori Probability (MAP) and Empirical Likelihood (EL) are shown to possess, under misspecification, an exclusive property of Bayesian consistency. Under conditions of consistency, regardless of prior the MAP estimator asymptotically coincides with EL. The consistency property is also studied for sampling processes other than iid.

ESTIMATING THE SIZE DISTRIBUTION OF FIRMS USING GOVERNMENT SUMMARY STATISTICS

Palavras-chave: Research Methods/ Statistical Methods.

Ano: 2008

URL: http://purl.umn.edu/6053

Golan, Amos; Judge, George G.; Perloff, Jeffrey M..

Using a maximum entropy technique, we estimate the market shares of each firm in an industry using the available government summary statistics such as the four-firm concentration ratio (C4) and the Herfindahl-Hirschmann Index (HHI). We show that our technique is very effective in estimating the distribution of market shares in 20 industries. Our results provide support for the recent practice of using HHI rather than C4 as the key explanatory variable in many market power studies, if only one measure is to be used.

A Semi-Parametric Basis for Combining Estimation Problems Under Quadratic Loss

Palavras-chave: Industrial Organization; Marketing.

Ano: 1995

URL: http://purl.umn.edu/25081

Judge, George G.; Mittelhammer, Ronald C..

When there is uncertainty concerning the appropriate statistical model to use in representing the data sampling process and corresponding estimators, we consider a basis for optimally combining estimation problems. In the context of the multivariate linear statistical model, we consider a semi-parametric Stein-like (SPSL) estimator, ...that shrinks to a random data-dependent vector and, under quadratic loss, has superior performance relative to the conventional least squares estimator. The relationship of the SPSL estimator to the family of Stein estimators is noted and risk dominance extensions between correlated estimators are demonstrated. As an application we consider the problem of a possibly ill-conditioned design matrix and devise...

ENTROPY-BASED ESTIMATION AND INFERENCE IN BINARY RESPONSE MODELS UNDER ENDOGENEITY

Palavras-chave: Stein-like shrinkage; Quadratic loss; Ill-conditioned design; Semiparametric estimation and inference; Data dependent shrinkage vector; Asymptotic and finite sample risk.; Research Methods/ Statistical Methods; Cl0; C24.

Ano: 2003

URL: http://purl.umn.edu/25103

Miller, Douglas J.; Mittelhammer, Ronald C.; Judge, George G..

This paper considers estimation and inference for the binary response model in the case where endogenous variables are included as arguments of the unknown link function. Semiparametric estimators are proposed that avoid the parametric assumptions underlying the likelihood approach as well as the loss of precision when using nonparametric estimation. Suggestions are made for how the utility maximization decision model can be altered to permit attributes to vary across alternatives.

Tipo: Conference Paper or Presentation

Palavras-chave: Research Methods/ Statistical Methods.

Ano: 2004

URL: http://purl.umn.edu/20319

A Bayesian Large Deviations Probabilistic Interpretation and Justification of Empirical Likelihood

In this paper we demonstrate, in a parametric Estimating Equations setting, that the Empirical Likelihood (EL) method is an asymptotic instance of the Bayesian non-parametric Maximum-A-Posteriori approach. The resulting probabilistic interpretation and justifcation of EL rests on Bayesian non-parametric consistency in L-divergence.

Some Empirical Evidence on the Impact of Measurement Errors in Making Ecological Inferences

Palavras-chave: Research Methods/ Statistical Methods.

Ano: 2007

URL: http://purl.umn.edu/7191

Cho, Wendy K.; Judge, George G..

We seek to identify the impact of data measurement error problems in the context of ecological inference applications. We explore the statistical and substantive implications of using inaccurate proxy variables in the estimation and inference process. The focus of our analysis is on applications of ecological inference in cases involving the Voting Rights Act. We demonstrate our findings with a unique data set on racial registration and turnout in Louisiana and South Carolina.

Estimating the size distribution of firms using government summary statistics

Palavras-chave: Ecological inference; Maximum entropy; Voting rights; Environmental Economics and Policy.

Ano: 2003

URL: http://purl.umn.edu/25080

Golan, Amos; Judge, George G.; Perloff, Jeffrey M..

Stigler's approach to recovering the distribution of first significant digits in natural data sets

Palavras-chave: Business; Entropy; Industry size; Marketing; Probabilities; Statistics; Agribusiness.

Ano: 1995

URL: http://purl.umn.edu/47276

Lee, Joanne; Cho, Wendy K.; Judge, George G..

In 1881, Newcomb conjectured that the first significant digits (FSDs) of numbers in statistical tables would follow a logarithmic distribution with the digit “1” occurring most often. However, because Newcomb’s proposal was not presented with a theoretical basis, it was not given much attention. Fifty-seven years later, Benford argued for the same principle and showed it was relevant to a large range of data sets, and the logarithmic FSD distribution became known as “Benford’s Law.” In the mid-1940s, Stigler claimed Benford’s Law contained a theoretical inconsistency and supplied an alternative derivation for the distribution of FSDs. In this paper, we examine the theoretical basis of the Stigler distribution and extend his reasoning by incorporating FSD...

An Information Theoretic Approach to Ecological Estimation and Inference

Palavras-chave: Benford's law; Stigler's law; Power law; Maximum entropy; Distance measures; Research and Development/Tech Change/Emerging Technologies; Research Methods/ Statistical Methods; C10; C24.

Ano: 2009

URL: http://purl.umn.edu/47000

Judge, George G.; Miller, Douglas J.; Cho, Wendy K..

MARKOV CHAINS: BASIC CONCEPTS AND SUGGESTED USES IN AGRICULTURAL ECONOMICS

Palavras-chave: Environmental Economics and Policy.

Ano: 2003

URL: http://purl.umn.edu/25065

Judge, George G.; Swanson, E.R..

Agricultural economists are often interested in characterizing or summarizing how economic processes and institutions have changed through time as well as what paths they are likely to take in future time periods. Given this interest or objective, we are therefore interested in methods of analysis that will accomplish these purposes and that are simple to apply. Within this context the major purpose of this paper is to discuss the concept of a Markov chain process and to indicate its potential usefulness in analyzing problems where detailed time-ordered data exist over some time span. As a particular vehicle for the discussion, a limited example concerning the past and potential size distribution of a sample of hog-producing firms in central Illinois will...

Tipo: Journal Article

Palavras-chave: Research Methods/ Statistical Methods.

Ano: 1962

URL: http://purl.umn.edu/22465

EMPIRICAL LIKELIHOOD ESTIMATORS OF THE LINEAR SIMULTANEOUS EQUATIONS MODEL

Marsh, Thomas L.; Mittelhammer, Ronald C.; Judge, George G..

Information theoretic estimators are specified for a system of linear simultaneous equations, including maximum empirical likelihood, maximum empirical exponential likelihood, and maximum log Euclidean likelihood. Monte Carlo experiments are used to compare finite sample performance of these estimators to traditional generalized method of moments.

Tipo: Conference Paper or Presentation

Palavras-chave: Research Methods/ Statistical Methods.

Ano: 2001

URL: http://purl.umn.edu/20752

Large Deviations Approach to Bayesian Nonparametric Consistency: the Case of Polya Urn Sampling

Grendar, Marian; Judge, George G.; Niven, R.K..

The Bayesian Sanov Theorem (BST) identifies, under both correct and incorrect specification of infinite dimensional model, the points of concentration of the posterior measure. Utilizing this insight in the context of Polya urn sampling, Bayesian nonparametric consistency is established. Polya BST is also used to provide an extension of Maximum Non-parametric Likelihood and Empirical Likelihood methods to the Polya case.

A Minimum Power Divergence Class of CDFs and Estimators for Binary Choice Models

Palavras-chave: Polya L-divergence; Bayesian maximum (A posterior); Probability method; Maximum Non-Parametric Likelihood method; Empirical likelihood method; Research Methods/ Statistical Methods.

Ano: 2007

URL: http://purl.umn.edu/6056

Mittelhammer, Ronald C.; Judge, George G..

The Cressie-Read (CR) family of power divergence measures is used to identify a new class of statistical models and estimators for competing explanations of the data in binary choice models. A large flexible class of cumulative distribution functions and associated probability density functions emerge that subsumes the conventional logit model, and forms the basis for a large set of estimation alternatives to traditional logit and probit methods. Asymptotic properties of estimators are identified, and sampling experiments are used to provide a basis for gauging the finite sample performance of the estimators in this new class of statistical models.