Applications of Information Measures to Assess Convergence in the Central Limit Theorem

Ranjani Atukorala (ranjani.atukorala@rmit.edu.au), Maxwell King and Sivagowry Sriananthakumar (sivagowry.sriananthakumar@rmit.edu.au)

No 29/14, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: The Central Limit Theorem (CLT) is an important result in statistics and econometrics and econometricians often rely on the CLT for inference in practice. Even though, different conditions apply to different kinds of data, the CLT results are believed to be generally available for a range of situations. This paper illustrates the use of the Kullback-Leibler Information (KLI) measure to assess how close an approximating distribution is to a true distribution in the context of investigating how different population distributions affect convergence in the CLT. For this purpose, three different non-parametric methods for estimating the KLI are proposed and investigated. The main findings of this paper are 1) the distribution of the sample means better approximates the normal distribution as the sample size increases, as expected, 2) for any fixed sample size, the distribution of means of samples from skewed distributions converges faster to the normal distribution as the kurtosis increases, 3) at least in the range of values of kurtosis considered, the distribution of means of small samples generated from symmetric distributions is well approximated by the normal distribution, and 4) among the nonparametric methods used, Vasicek's (1976) estimator seems to be the best for the purpose of assessing asymptotic approximations. Based on the results of the paper, recommendations on minimum sample sizes required for an accurate normal approximation of the true distribution of sample means are made.

Keywords: Kullback-Leibler Information; Central Limit Theorem; skewness and kurtosis (search for similar items in EconPapers)
JEL-codes: C1 C2 C4 C5 (search for similar items in EconPapers)
Date: 2014
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://business.monash.edu/__data/assets/pdf_file/0008/327176/wp29-14.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://business.monash.edu/__data/assets/pdf_file/0008/327176/wp29-14.pdf [301 Moved Permanently]--> https://business.monash.edu/__data/assets/pdf_file/0008/327176/wp29-14.pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:msh:ebswps:2014-29

Ordering information: This working paper can be ordered from
http://business.mona ... -business-statistics
econometrics@monash.edu

Access Statistics for this paper

More papers in Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics PO Box 11E, Monash University, Victoria 3800, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Professor Xibin Zhang (xibin.zhang@monash.edu).