By George G. Judge
This booklet is meant to supply the reader with a company conceptual and empirical figuring out of uncomplicated information-theoretic econometric versions and strategies. simply because so much facts are observational, practitioners paintings with oblique noisy observations and ill-posed econometric versions within the kind of stochastic inverse difficulties. hence, conventional econometric tools in lots of situations aren't appropriate for answering a few 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 relations of strength divergence measure-likelihood services are brought for a number conventional and nontraditional econometric-model difficulties. ultimately, inside of both an empirical greatest chance or loss context, Ron C. Mittelhammer and George G. pass judgement on recommend a foundation for selecting a member of the divergence relations
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Extra resources for An Information Theoretic Approach to Econometrics
The tests are asymptotically equivalent, meaning that their asymptotic distributions are identical; thus, a choice between them cannot be made on the basis of their asymptotic behavior. The W test is based on the unrestricted (by H0 ) LS estimator, whereas the LM test is based on the restricted (by H0 ) LS estimator. Based on the duality between hypothesis tests and confidence region estimation, W and LM-based confidence regions can be defined that have predefined asymptotic levels of confidence for covering the true value of cβ.
Of course, this is completely general because we can minimize an objective function by maximizing the negative of the same objective function. The properties of an E estimator depend on the properties of the estimation metric or estimation objective function being optimized. For the metrics commonly used in econometric practice, the properties of consistency and asymptotic normality are achieved under general regularity conditions relating to D. Given the wide variety of different choices that are possible for the estimation objective function component of the E estimation problem, there are no broad finite sample property generalizations that can be made for E estimators, and so our focus vis-`a-vis general sampling properties is restricted to asymptotic properties.
6) where the estimation objective function is defined specifically as m(θ, Y, x) ≡ L (θ ; Y, x). 7) Recognizing that the ML estimator is in the class of E estimators allows us to transfer the general asymptotic results for E estimation to the case of ML estimation. 2 the issue of the consistency and asymptotic normality of the ML or bias-adjusted ML estimator of β and σ 2 in the context of the multivariate normal linear model. In the context of E estimation, one can establish and motivate more general results that can be applied to ML estimation problems in other parametric probability models.
An Information Theoretic Approach to Econometrics by George G. Judge