By George G. Judge
This ebook is meant to supply the reader with an organization conceptual and empirical realizing of uncomplicated information-theoretic econometric types and strategies. simply because so much info are observational, practitioners paintings with oblique noisy observations and ill-posed econometric versions within the type of stochastic inverse difficulties. for this reason, conventional econometric equipment in lots of instances aren't appropriate for answering a number of the quantitative questions that analysts desire to ask. After preliminary chapters care for parametric and semiparametric linear likelihood versions, the focal point turns to fixing nonparametric stochastic inverse difficulties. In succeeding chapters, a relations of energy divergence measure-likelihood services are brought for a number conventional and nontraditional econometric-model difficulties. ultimately, inside 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 kinfolk. [C:\Users\Microsoft\Documents\Calibre Library]
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Extra resources for An Information Theoretic Approach to Econometrics Paperback
We noted earlier that the ML criterion for estimating θ is subsumed under the E estimation concept. 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.
3. These assumptions are sufficient conditions. Weaker conditions leading to the validity of the standard testing procedures can be found in White (1984). Confidence regions can then be based on duality with the hypothesis testing procedures, again precisely as they were defined previously. 1 relating to the parametric framework apply as well to the case where X is stochastic. 12 on Tue Oct 09 05:48:27 BST 2012. 4 General Linear Model with Stochastic X 29 when considering finite sample properties of test and confidence region procedures, and so we examine more of the details for this case here.
12 on Tue Oct 09 05:48:27 BST 2012. 3 A Semiparametric General Linear Model 21 properties of βˆ . 13) is an unbiased estimator of σ 2 and assuming that the noise terms are iid, p S2 → σ 2 , so that S2 is a consistent estimator. Under higher order moment assumptions relating to the εi s, S2 is asymptotically normally distributed with mean σ 2 and asymptotic variance (μ′4 − σ 4 )/n, where μ′4 is the fourth moment of the εi s. 6 Inferential Asymptotics Because we make no specific distributional assumptions relating to ε or Y in the current semiparametric probability model, it should come as no surprise that hypothesis testing and confidence region estimation procedures must be based on approximate or asymptotic distributions of statistics.
An Information Theoretic Approach to Econometrics Paperback by George G. Judge