Tursunov, G. T. On estimation of the asymptotic variance of rank estimates of the location parameter from a sample of random size. (Russian) Zbl 0689.62019 Teor. Sluch. Protsess. 15, 97-102 (1987). 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. Reviewer: S. Csörgö (M.R. 88h:62081) Cited in 1 Review MSC: 62E20 Asymptotic distribution theory in statistics 62G15 Nonparametric tolerance and confidence regions Keywords:asymptotic normality; asymptotic variance of the Hodges-Lehmann estimator of a location; sequential confidence intervals PDFBibTeX XMLCite \textit{G. T. Tursunov}, Teor. Sluch. Protsess. 15, 97--102 (1987; Zbl 0689.62019)