By George G. Judge
This booklet is meant to supply the reader with an organization conceptual and empirical realizing of simple information-theoretic econometric versions and techniques. simply because such a lot info are observational, practitioners paintings with oblique noisy observations and ill-posed econometric versions within the kind of stochastic inverse difficulties. accordingly, conventional econometric tools in lots of situations aren't appropriate for answering a number of the quantitative questions that analysts desire to ask. After preliminary chapters take care of parametric and semiparametric linear likelihood types, the focal point turns to fixing nonparametric stochastic inverse difficulties. In succeeding chapters, a relatives of strength divergence measure-likelihood services are brought for more than a few conventional and nontraditional econometric-model difficulties. eventually, inside of both an empirical greatest probability or loss context, Ron C. Mittelhammer and George G. pass judgement on recommend a foundation for selecting a member of the divergence family members
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Additional info for An Information Theoretic Approach to Econometrics
6) i=1 where y denotes an outcome of Y. 6) to solve for θ and thereby obtain information about the value of θ. 5), we will have derived the true value, θ0 , of the unknown θ and our estimate of the value of the parameter vector would be perfect. We emphasize that “true value” here means the value of θ that indexes the probability distribution for which the outcomes from D are actually sampled. 6). If the Yi s are iid, then the h(Yi , θ)’s are also iid and one could invoke Khinchin’s weak law of large numbers to claim that the sample estimate converges to the true value of the moment equap tions, as n−1 ni=1 h∗ (Yi , θ) → E [h∗ (Y, θ)].
J. (1981), Robust Statistics. New York: John Wiley and Sons. Lehmann, E. and G. Casella (1998), Theory of Point Estimation. New York: SpringerVerlag. McCullagh, P. and J. A. Nelder (1989), Generalized Linear Models, 2nd ed. London: Chapman and Hall. Mittelhammer, R. C. (1996), Mathematical Statistics for Economics and Business. New York: Springer-Verlag. , G. Judge, and D. Miller (2000), Econometric Foundations. New York: Cambridge University Press. Newey, W. K. and D. McFadden (1994), “Large Sample Estimation and Hypothesis Testing,” in Handbook of Econometrics, edited by Robert F.
Under both independent and contemporaneously uncorrelated X and ε, with E [ε |X] = 0, the LS estimator is unconditionally unbiased, its unconditional covariance matrix is σ 2 E [(X X)−1 ], and S 2 = (Y − Xβˆ ) (Y − Xβˆ )/(n − k) is an unconditionally unbiased estimator of the noise component variance. 3. If ε is multivariate normally distributed and the distribution of X 2 = does not depend on β or σ 2 , then βˆ = (X X)−1 X Y and S ML 2 ˆ ˆ (Y − Xβ) (Y − Xβ)/n are the ML estimators of β and σ .
An Information Theoretic Approach to Econometrics by George G. Judge