### An Efficient Estimator Using Auxiliary Information.

A. Sahai, S.K. Ray (1980)

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A. Sahai, S.K. Ray (1980)

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S.G. Prabhu-Ajgaonkar (1984)

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T.J. Rao (1972)

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A. Chaudhuri (1976)

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Mokkadem, Abdelkader, Mariane, Pelletier, Baba, Thiam (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 62G07, 60F10. In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic behaviour not only for the moderate deviations scale but also for the large deviations one. We provide results both for the pointwise and the uniform deviations.

Nicolas W. Hengartner, Éric Matzner-Løber (2009)

ESAIM: Probability and Statistics

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This paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as , where we see an improvement of as much as 20% over the traditionnal estimator. ...

V.K. Srivastava, A. Chaturvedi (1983)

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M.T. Subrahmanya (1967/68)

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Csiszár, Imre, Shields, Paul C. (1999)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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N.D. Shukla (1976)

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K. Takeuchi, M. Akahira (1987)

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S.G. Prabhu Ajgaonkar (1972)

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Y.P. Chaubey, M. Singh, T.D. Dwivedi (1990)

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Th. Pfaff (1983)

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Stéphane Girard, Armelle Guillou, Gilles Stupfler (2014)

ESAIM: Probability and Statistics

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We consider the high order moments estimator of the frontier of a random pair, introduced by [S. Girard, A. Guillou and G. Stupfler, 116 (2013) 172–189]. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.