NDLI: Uniform integrability of the OLS estimators, and the convergence of their moments

Content Provider	Springer Nature Link
Author	Afendras, Georgios Markatou, Marianthi
Copyright Year	2016
Abstract	The problem of convergence of moments of a sequence of random variables to the moments of its asymptotic distribution is important in many applications. These include the determination of the optimal training sample size in the cross-validation estimation of the generalization error of computer algorithms, and in the construction of graphical methods for studying dependence patterns between two biomarkers. In this paper, we prove the uniform integrability of the ordinary least squares estimators of a linear regression model, under suitable assumptions on the design matrix and the moments of the errors. Further, we prove the convergence of the moments of the estimators to the corresponding moments of their asymptotic distribution, and study the rate of the moment convergence. The canonical central limit theorem corresponds to the simplest linear regression model. We investigate the rate of the moment convergence in canonical central limit theorem proving a sharp improvement of von Bahr’s (Ann Math Stat 36:808–818, 1965) theorem.
Starting Page	775
Ending Page	784
Page Count	10
File Format	PDF
ISSN	11330686
Journal	Test
Volume Number	25
Issue Number	4
e-ISSN	18638260
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-07-05
Publisher Institution	Spanish Society of Statistics and Operations Research
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Linear regression model Moment convergence Rate of convergence Uniform integrability Linear regression Asymptotic distribution theory Inequalities; stochastic orderings Central limit and other weak theorems Factorials, binomial coefficients, combinatorial functions Statistics Statistical Theory and Methods Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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