Displaying similar documents to “Asymptotic unbiased density estimators”

Plug-in estimators for higher-order transition densities in autoregression

Anton Schick, Wolfgang Wefelmeyer (2009)

ESAIM: Probability and Statistics

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In this paper we obtain root- consistency and functional central limit theorems in weighted -spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based...

A Cramer-Rao analogue for median-unbiased estimators.

N. K. Sung, Gabriela Stangenhaus, Herbert T. David (1990)

Trabajos de Estadística

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Adopting a measure of dispersion proposed by Alamo [1964], and extending the analysis in Stangenhaus [1977] and Stangenhaus and David [1978b], an analogue of the classical Cramér-Rao lower bound for median-unbiased estimators is developed for absolutely continuous distributions with a single parameter, in which mean-unbiasedness, the Fisher information, and the variance are replaced by median-unbiasedness, the first absolute moment of the sample score, and the reciprocal of twice the...

A review of the results on the Stein approach for estimators improvement.

Vassiliy G. Voinov, Mikhail S. Nikulin (1995)

Qüestiió

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Since 1956, a large number of papers have been devoted to Stein's technique of obtaining improved estimators of parameters, for several statistical models. We give a brief review of these papers, emphasizing those aspects which are interesting from the point of view of the theory of unbiased estimation.

An alternative analysis of variance.

Nicholas T. Longford (2008)

SORT

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The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative.

Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

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.

Empirical comparison between the Nelson-Aalen Estimator and the Naive Local Constant Estimator.

Ana María Pérez-Marín (2008)

SORT

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The Nelson-Aalen estimator is widely used in biostatistics as a non-parametric estimator of the cumulative hazard function based on a right censored sample. A number of alternative estimators can be mentioned, namely, the naive local constant estimator (Guillén, Nielsen and Pérez-Marín, 2007) which provides improved bias versus variance properties compared to the traditional Nelson-Aalen estimator. Nevertheless, an empirical comparison of these two estimators has never been carried out....

Estimating quantiles with Linex loss function. Applications to VaR estimation

Ryszard Zieliński (2005)

Applicationes Mathematicae

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Sometimes, e.g. in the context of estimating VaR (Value at Risk), underestimating a quantile is less desirable than overestimating it, which suggests measuring the error of estimation by an asymmetric loss function. As a loss function when estimating a parameter θ by an estimator T we take the well known Linex function exp{α(T-θ)} - α(T-θ) - 1. To estimate the quantile of order q ∈ (0,1) of a normal distribution N(μ,σ), we construct an optimal estimator in the class of all estimators...

Efficiency rate and local deficiency of Huber's location estimators and of the α-estimators.

Asunción Rubio, Jan Amos Visek (1991)

Trabajos de Estadística

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The paper studies the problem of selecting an estimator with (approximately) minimal asymptotic variance. For every fixed contamination level there is usually just one such estimator in the considered family. Using the first and the second derivative of the asymptotic variance with respect to the parameter which parametrizes the family of estimators the paper gives two examples of how to select the estimator and gives an approximation to a loss which we suffer when we use the estimator...