Summary
Fór the estimation of the functional Δ (f)=∫f 2(x)dx Bhattacharyya andRoussas [1969] proposed an estimator based on the kernel-technique for density estimation. This paper describes a method, which rests on density estimations by orthogonal expansions. In the main we show the considered estimator to be consistent in the quadratic mean.
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Literatur
Bhatacharyya, G.K., undG.G. Roussas: Estimation of a certain functional of a probability density function. Skand. Aktuarietidskr., vol.3–4, 201–206, 1969.
Čencov, N.N.: Evaluation of an unknown distribution density from observations. Soviet. Math., vol.3, 1559–1562, 1962.
Kronmal, R., undM. Tarter: The estimation of probability densities and cumulatives by fourier series methods. J.Amer.Statist.Assoc., vol.63, 925–952, 1968.
Parzen, E.: On estimation of a probability density function and mode. Ann.Math.Statist., vol.33, 1065–1076, 1962.
Rosenblatt, M.: Remarks on some nonparametric estimates of a density function. Ann.Math.Statist., vol.27, 832–837, 1954.
Schwartz, S.C.: Estimation of probability density by orthogonal series. Ann.Math.Statist., vol.38, 1261–1265, 1967.
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Schüler, L., Wolff, H. Zur Schätzung eines Dichtefunktionals. Metrika 23, 149–154 (1976). https://doi.org/10.1007/BF01902859
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DOI: https://doi.org/10.1007/BF01902859