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Consistency of a nonparametric estimation of a density functional. (English) Zbl 0517.62043


MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62G10 Nonparametric hypothesis testing
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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
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