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2326 results in Statistical theory and methods

Page 31 of 117

  • Introduction

  • Olivier Compte, Andrew Postlewaite, University of Pennsylvania
  • Book:
    Ignorance and Uncertainty
    Published online:
    30 November 2018
    Print publication:
    13 December 2018, pp 1-6
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Ignorance and Uncertainty
  • Olivier Compte, Andrew Postlewaite
  • Published online:
    30 November 2018
    Print publication:
    13 December 2018
  • Born of a belief that economic insights should not require much mathematical sophistication, this book proposes novel and parsimonious methods to incorporate ignorance and uncertainty into economic modeling, without complex mathematics. Economics has made great strides over the past several decades in modeling agents' decisions when they are incompletely informed, but many economists believe that there are aspects of these models that are less than satisfactory. Among the concerns are that ignorance is not captured well in most models, that agents' presumed cognitive ability is implausible, and that derived optimal behavior is sometimes driven by the fine details of the model rather than the underlying economics. Compte and Postlewaite lay out a tractable way to address these concerns, and to incorporate plausible limitations on agents' sophistication. A central aspect of the proposed methodology is to restrict the strategies assumed available to agents.

  • 10 - Asymptotic theory

  • from Part B - Estimation And Inference
  • Karim M. Abadir, Imperial College London, Risto D. H. Heijmans, Jan R. Magnus, Vrije Universiteit, Amsterdam
  • Book:
    Statistics
    Published online:
    11 June 2020
    Print publication:
    08 November 2018, pp 371-436

  • Summary

    It is clear from the previous chapter that sample statistics have distributions depending, in general, on the sample size n. The natural question one may ask is how these distributions are affected by varying n deterministically and, in particular, as n increases. It turns out that one can get common limiting results, for a variety of settings, by analyzing what happens as n tends to infinity; this is large-sample asymptotic theory.We study convergence of distributions and of characteristic functions. For variates that converge to a single value, we study convergence in probability and in moments, and almost-sure convergence with its connection to events that happen infinitely-often. The speed of convergence and orders of magnitude are covered, as are law of large numbers (LLNs) weak and strong, limiting distributions such as central limit theorems (CLTs), stable limit theorems (SLTs), the generalized extreme-value theorem with its three special cases, and a law of iterated logarithms.

Page 31 of 117