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Evolution equations --- Asymptotic theory --- Asymptotic theory. --- Evolution equations - Asymptotic theory
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The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis.Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.
Econometrics --- Asymptotic theory --- Econometrics - Asymptotic theory
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"In the usage of present-day statistics 'statistical inference' is a profoundly ambiguous expression. In some literature a statistical inference is a "decision made under risk', in other literature it is 'a conclusion drawn from given data', and most of the literature displays no awareness that the two meanings might be different. This book concerns the problem of drawing conclusions from given data, in which respect we have to ask: Does there exist a need for the term 'statistical inference'? If so, does there also exist a corresponding need for every other science? If so, how does, for example, agronomy then manage to reason in terms of botanical inference, soil scientific inference, meteorological inference, biochemical inference, molecular biological inference, entomological inference, plant pathological inference, etc. without incoherence or self-contradiction? Consider the possibility that agronomy does not reason in terms of such a motley of special kinds of inference. Consider the possibility that, apart from subject matter, botany, soil science, entomology, etc. all employ the same kind of reasoning. If so, must we then believe that statistics, alone among all the sciences, is the only one that requires its own special kind of inference?"--Page i.
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We examine the implications of arbitrage in a market with many assets. The absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous; hence there exist unique portfolios that represent these functionals. The mean variance efficient set is a cone generated by these portfolios. Ross [16, 18J showed that if there is a factor structure, then the distance between the vector or mean returns and the space spanned by the factor loadings is bounded as the number of assets increases. We show that if the covariance matrix of asset returns has only K unbounded eigenvalues, then the corresponding K eigenvectors converge and play the role of factor loadings in Ross' result. Hence only a principal components analysis is needed to test the arbitrage pricing theory. Our eigenvalue conditional can hold even though conventional measures of the approximation error in a K factor model are unbounded. We also resolve the question of when a market with many assets permits so much diversification that risk-free investment opportunities are available.
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Mathematical statistics --- Sampling (Statistics) --- Asymptotic theory. --- Asymptotic theory
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Mathematical statistics --- Asymptotic theory --- Congresses
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