An Information Theoretic Approach to Econometrics
This book is intended to provide the reader with a firm conceptual and empirical understanding of basic information-theoretic econometric models and methods. Because most data are observational, practitioners work with indirect noisy observations and ill-posed econometric models in the form of stochastic inverse problems. Consequently, traditional econometric methods in many cases are not applicable for answering many of the quantitative questions that analysts wish to ask. After initial chapters deal with parametric and semiparametric linear probability models, the focus turns to solving nonparametric stochastic inverse problems. In succeeding chapters, a family of power divergence measure-likelihood functions are introduced for a range of traditional and nontraditional econometric-model problems. Finally, within either an empirical maximum likelihood or loss context, Ron C. Mittelhammer and George G. Judge suggest a basis for choosing a member of the divergence family.
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ˆ β ˆβ(γ applied approach assumptions asymptotic normality binary response model Chapter Chi-square Chi-square distribution choice confidence region consistent estimator constraints context convex combination covariance matrix CR family Cressie-Read data sampling process defined denotes divergence measures econometric econometric model EE estimator empirical likelihood empirical probability entropy esti estimating equations estimating functions estimation and inference estimation objective function estimation problem extremum finite sample functional form given GMM estimator hypothesis testing indirect noisy observations KL information Lagrange multiplier likelihood function linear model ln(pi maximizing maximum empirical maximum likelihood MEEL method of moments minimizing Mittelhammer ML estimator nonparametric objective function OptEF optimal parameter vector power divergence probability distribution probability weights procedures random variables reference distribution regularity conditions sampling properties scalar semiparametric solution solving specification stochastic inverse problem testing and confidence tion unbiased underlying unknown parameters variance