By George G. Judge

ISBN-10: 0521689732

ISBN-13: 9780521689731

ISBN-10: 0521869595

ISBN-13: 9780521869591

This ebook is meant to supply the reader with a company conceptual and empirical knowing of simple information-theoretic econometric types 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. for this reason, conventional econometric tools in lots of instances should not acceptable for answering a few of the quantitative questions that analysts desire to ask. After preliminary chapters care for parametric and semiparametric linear chance versions, the focal point turns to fixing nonparametric stochastic inverse difficulties. In succeeding chapters, a relations of strength divergence measure-likelihood services are brought for quite a number conventional and nontraditional econometric-model difficulties. eventually, inside 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 kinfolk

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**Additional resources for An Information Theoretic Approach to Econometrics**

**Example text**

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 . 4. The asymptotic properties of the LS estimators when X is stochastic, as well as properties for the ML estimator under conditional normality of (Y|x) and weak exogeneity of X, follow those established for the case when the x’s are fixed. 5. 1. 6. 1. ” In fact, the E estimators represent a class of estimators that encompass most of the estimators used in econometric practice.

In practice, the proportionality factor is generally taken to be 1. 2) where Y is an (n × 1) random dependent variable vector, x is an (n × k) nonstochastic explanatory variable matrix, β is a (k × 1) vector of unknown parameters, and σ2 is a scalar unknown parameter. 1). The information-recovery problem is one of using observations on sample data outcomes, y, given the associated fixed and known values of x, to generate information on (estimates of) the k + 1 unknowns θ = {β, σ 2 }. 2) that are applicable to the DSP.

The GLR statistic has an asymptotic Chi-square distribution under generally applicable regularity conditions with degrees of freedom equal to the number of functionally independent restrictions on the parameter vector implied by the null hypothesis θ ∈ H0 . , unaffected) by any 1-to-1 functional transformations of the parameter space. Other popular tests in econometric practice, including the Lagrange multiplier and W tests (discussed in Section 2), do not necessarily possess the invariance property.

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