Exceptional Convergence of the Sample Variance

T.S.K. Moothathu

Statistica Neerlandica, 1987, vol. 41, issue 4, 253-256

Abstract: The case is investigated when Hoeffding's one sample U–statistic theorem for the sample variance S2 is not applicable. It is shown that this occurs only when the parent distribution is the two–point distribution with jumps of equal magnitude. For this exceptional case the standardised S2 is shown to converge in distribution to (1 –V)√2, where V has chi–square distribution with one degree of freedom.

Date: 1987
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