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Rank tests of symmetry and R-estimation of location parameter under measurement errors

Radim Navrátil (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper deals with the hypotheses of symmetry of distributions with respect to a location parameter when the response variables are subject to measurement errors. Rank tests of hypotheses about the location parameter and the related R-estimators are studied in an asymptotic set up. It is shown, when and under what conditions, these rank tests and R-estimators can be used effectively, and the effect of measurement errors on the power of the test and on the efficiency of the R-estimators is indicated....

Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study

A. K. Md. Ehsanes Saleh, Radim Navrátil (2018)

Kybernetika

In the development of efficient predictive models, the key is to identify suitable predictors for a given linear model. For the first time, this paper provides a comparative study of ridge regression, LASSO, preliminary test and Stein-type estimators based on the theory of rank statistics. Under the orthonormal design matrix of a given linear model, we find that the rank based ridge estimator outperforms the usual rank estimator, restricted R-estimator, rank-based LASSO, preliminary test and Stein-type...

Recursive estimates of quantile based on 0-1 observations

Pavel Charamza (1992)

Applications of Mathematics

The objective of this paper is to introduce some recursive methods that can be used for estimating an L D - 50 value. These methods can be used more generally for the estimation of the γ -quantile of an unknown distribution provided we have 0-1 observations at our disposal. Standard methods based on the Robbins-Monro procedure are introduced together with different approaches of Wu or Mukerjee. Several examples are also mentioned in order to demonstrate the usefulness of the methods presented.

Remarks on optimum kernels and optimum boundary kernels

Jitka Poměnková (2008)

Applications of Mathematics

Kernel smoothers belong to the most popular nonparametric functional estimates used for describing data structure. They can be applied to the fix design regression model as well as to the random design regression model. The main idea of this paper is to present a construction of the optimum kernel and optimum boundary kernel by means of the Gegenbauer and Legendre polynomials.

Risk bounds for mixture density estimation

Alexander Rakhlin, Dmitry Panchenko, Sayan Mukherjee (2005)

ESAIM: Probability and Statistics

In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Estimator (MLE) and the greedy procedure described by Li and Barron (1999) under the additional assumption of boundedness of densities. We prove an O ( 1 n ) bound on the estimation error which does not depend on the number of densities in the estimated combination. Under the boundedness assumption, this improves the bound of Li and Barron by...

Risk bounds for mixture density estimation

Alexander Rakhlin, Dmitry Panchenko, Sayan Mukherjee (2010)

ESAIM: Probability and Statistics

In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Estimator (MLE) and the greedy procedure described by Li and Barron (1999) under the additional assumption of boundedness of densities. We prove an O ( 1 n ) bound on the estimation error which does not depend on the number of densities in the estimated combination. Under the boundedness assumption, this improves the bound of Li and Barron...

Risk hull method for spectral regularization in linear statistical inverse problems

Clément Marteau (2010)

ESAIM: Probability and Statistics

We consider in this paper the statistical linear inverse problem Y = Af + ϵξ where A denotes a compact operator, ϵ a noise level and ξ a stochastic noise. The unknown function f has to be recovered from the indirect measurement Y. We are interested in the following approach: given a family of estimators, we want to select the best possible one. In this context, the unbiased risk estimation (URE) method is rather popular. Nevertheless, it is also very unstable. Recently, Cavalier and Golubev (2006)...

Robust estimation based on spacings in weighted exponential models

Paweł Błażej, Jarosław Bartoszewicz (2007)

Applicationes Mathematicae

Using Zieliński's (1977, 1983) formalization of robustness Błażej (2007) obtained uniformly most bias-robust estimates (UMBREs) of the scale parameter for some statistical models (including the exponential model), in a class of linear functions of order statistics, when violations of the models are generated by weight functions. In this paper the UMBRE of the scale parameter, based on spacings, in two weighted exponential models is derived. Extensions of results of Bartoszewicz (1986, 1987) are...

Segmentation of the Poisson and negative binomial rate models: a penalized estimator

Alice Cleynen, Emilie Lebarbier (2014)

ESAIM: Probability and Statistics

We consider the segmentation problem of Poisson and negative binomial (i.e. overdispersed Poisson) rate distributions. In segmentation, an important issue remains the choice of the number of segments. To this end, we propose a penalized -likelihood estimator where the penalty function is constructed in a non-asymptotic context following the works of L. Birgé and P. Massart. The resulting estimator is proved to satisfy an oracle inequality. The performances of our criterion is assessed using simulated...

Semiparametric deconvolution with unknown noise variance

Catherine Matias (2002)

ESAIM: Probability and Statistics

This paper deals with semiparametric convolution models, where the noise sequence has a gaussian centered distribution, with unknown variance. Non-parametric convolution models are concerned with the case of an entirely known distribution for the noise sequence, and they have been widely studied in the past decade. The main property of those models is the following one: the more regular the distribution of the noise is, the worst the rate of convergence for the estimation of the signal’s density...

Semiparametric deconvolution with unknown noise variance

Catherine Matias (2010)

ESAIM: Probability and Statistics

This paper deals with semiparametric convolution models, where the noise sequence has a Gaussian centered distribution, with unknown variance. Non-parametric convolution models are concerned with the case of an entirely known distribution for the noise sequence, and they have been widely studied in the past decade. The main property of those models is the following one: the more regular the distribution of the noise is, the worst the rate of convergence for the estimation of the signal's density...

Sequential estimation of survival functions with a neutral to the right process prior

Domingo Morales, Leandro Pardo, Vicente Quesada (1994)

Applications of Mathematics

In this work, a parametric sequential estimation method of survival functions is proposed in the Bayesian nonparametric context when neutral to the right processes are used. It is proved that the mentioned method is an 1-SLA rule when Dirichlet processes are used; furthermore, asymptotically pointwise optimal procedures are obtained. Finally, an example is given.

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