Ahmad, I. A.; Lin, P.-E. Consistency of a nonparametric estimation of a density functional. (English) Zbl 0517.62043 Metrika 30, 21-29 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference 62G10 Nonparametric hypothesis testing Keywords:consistency; density functional; Chernoff-Savage statistic; kernel estimates; density estimation PDFBibTeX XMLCite \textit{I. A. Ahmad} and \textit{P. E. Lin}, Metrika 30, 21--29 (1983; Zbl 0517.62043) Full Text: DOI EuDML References: [1] Ahmad, I.A.: On the asymptotic properties of an estimate of a functional of a probability density. Scand. Actuarial J.4, 1976, 176–181. · Zbl 0354.62036 [2] Bhattacharayya, G.K., andG. Roussas: Estimation of a certain functional of a probability density function. Skand. Aktuar. Tidskr.52, 1969, 201–206. [3] Chernoff, H., andI.R. Savage: Asymptotic normality and efficiency of certain nonparametric test statistics. Ann. Math. Statist.29, 1958, 972–994. · Zbl 0092.36501 · doi:10.1214/aoms/1177706436 [4] Dvoretsky, A., J. Kiefer, andJ. Wolfowitz: Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Ann. Math. Statist.27, 1956, 642–669. · Zbl 0073.14603 · doi:10.1214/aoms/1177728174 [5] Nadaraya, E. A.: On nonparametric estimation of density functions and regression curves. Theor. Probability Appl.10, 1965, 186–190. · Zbl 0134.36302 · doi:10.1137/1110024 [6] Parzen, E.: On estimation of probability density function and mode. Ann. Math. Statist.33, 1962, 1065–1076. · Zbl 0116.11302 · doi:10.1214/aoms/1177704472 [7] Puri, M.L., andP.K. Sen: Nonparametric Methods in Multivariate Analysis. New York 1971. · Zbl 0237.62033 [8] Schuster, E.F.: On the rate of convergence of an estimate of a functional of a probability density. Scand. Actuarial J.2, 1974, 103–107. · Zbl 0285.62016 [9] Sen, P.K.: On a distribution-free method of estimating asymptotic efficiency of a class of nonparametric tests. Ann. Math. Statist.37, 1966, 1759–1770. · Zbl 0158.37201 · doi:10.1214/aoms/1177699164 [10] Van Ryzin, J.: On strong consistency of density estimates. Ann. Math. Statist.40, 1969, 1765–1772. · Zbl 0198.23502 · doi:10.1214/aoms/1177697388 [11] Winter, B.B.: Convergence rate of perturbed empirical distribution functions. J. Appl. Probability16, 1979, 163–173. · Zbl 0403.60033 · doi:10.2307/3213384 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.