Limit Theorems

Pham-Gia Thu

Chapter 3 in The Multivariate Normal Distribution:Theory and Applications, 2021, pp 35-52 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The following sections are included:IntroductionConvergence in DistributionConvergence in Probability (Stochastic or Weak Convergence)Laws of Large NumbersWeak law of large numbers (Bernoulli–Khintchine)Strong law of large numbersSLLN for simulationA famous application of the LLNCentral Limit TheoremDe Moivre–Laplace theoremLindenberg–Levy central limit theoremLiapounoff theoremLimit theorems for densitiesOther Types of ConvergenceAlmost sure convergenceConvergence in meanRelations between types of convergenceApproximationsCentral Limit Theorem for a Bivariate DistributionLimit Theorems and Distributions in the Multivariate CaseThe Berry–Esseen TheoremsLimiting Spectral DistributionApplicationsDie rollingThe binomial distribution and multiple choice testsConclusionBibliography

Keywords: Univariate Normal; Multivariate; Random Variable; Random Vector; Random Matrix; Applications: Education; Psychology; Quality Control; Pattern Recognition (search for similar items in EconPapers)
JEL-codes: C01 C1 C15 C4 C46 (search for similar items in EconPapers)
Date: 2021
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