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On estimation of the asymptotic variance of rank estimates of the location parameter from a sample of random size. (Russian) Zbl 0689.62019

Under some regularity conditions, the asymptotic normality of the standard estimator of the asymptotic variance of the Hodges-Lehmann estimator of a location parameter of a density function f is proved when the sample size is random and possibly depends on the sample itself. The result is then applied for the construction of sequential confidence intervals for the quantity \(\int f^ 2\) with some optimal properties.

MSC:

62E20 Asymptotic distribution theory in statistics
62G15 Nonparametric tolerance and confidence regions
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