Reasonable Sample Sizes for Convergence to Normality

9 Pages Posted: 18 Dec 2014

See all articles by Carsten Schröder

Carsten Schröder

Free University of Berlin (FUB) - Department of Business and Economics

Shlomo Yitzhaki

Hebrew University of Jerusalem - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: December 2014

Abstract

The central limit theorem says that, provided an estimator fulfills certain weak conditions, then, for reasonable sample sizes, the sampling distribution of the estimator converges to normality. We propose a procedure to find out what a “reasonably large sample size” is. The procedure is based on the properties of Gini’s mean difference decomposition. We show the results of implementations of the procedure from simulated datasets and data from the German Socio‐economic Panel.

Keywords: central limit theorem, Gini’s mean difference composition

JEL Classification: C1, C4

Suggested Citation

Schröder, Carsten and Yitzhaki, Shlomo, Reasonable Sample Sizes for Convergence to Normality (December 2014). SOEPpaper No. 714, Available at SSRN: https://ssrn.com/abstract=2539096 or http://dx.doi.org/10.2139/ssrn.2539096

Carsten Schröder (Contact Author)

Free University of Berlin (FUB) - Department of Business and Economics ( email )

Boltzmannstrasse 20
D-14195 Berlin, 14195
Germany
+49 030 838-52259 (Phone)
+49 030 838-52560 (Fax)

Shlomo Yitzhaki

Hebrew University of Jerusalem - Department of Economics ( email )

Mount Scopus
Jerusalem, 91905
Israel
+972 2 659 2201 (Phone)
+972 2 652 2319 (Fax)

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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