Displaying similar documents to “Estimation of second order parameters using probability weighted moments”

Estimation of second order parameters using probability weighted moments

Julien Worms, Rym Worms (2012)

ESAIM: Probability and Statistics

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The P.O.T. method (Peaks Over Threshold) consists in using the generalized Pareto distribution (GPD) as an approximation for the distribution of excesses over a high threshold. In this work, we use a refinement of this approximation in order to estimate second order parameters of the model using the method of probability-weighted moments (PWM): in particular, this leads to the introduction of a new estimator for the second order parameter , which will be compared to other recent estimators...

The law of the iterated logarithm for the multivariate kernel mode estimator

Abdelkader Mokkadem, Mariane Pelletier (2010)

ESAIM: Probability and Statistics

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Let be the mode of a probability density and its kernel estimator. In the case is nondegenerate, we first specify the weak convergence rate of the multivariate kernel mode estimator by stating the central limit theorem for . Then, we obtain a multivariate law of the iterated logarithm for the kernel mode estimator by proving that, with probability one, the limit set of the sequence suitably normalized is an ellipsoid. We also give a law of the iterated logarithm for the norms,...

Towards a universally consistent estimator of the Minkowski content

Antonio Cuevas, Ricardo Fraiman, László Györfi (2013)

ESAIM: Probability and Statistics

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We deal with a subject in the interplay between nonparametric statistics and geometric measure theory. The measure () of the boundary of a set  ⊂ ℝ (with  ≥ 2) can be formally defined, a simple limit, by the so-called Minkowski content. We study the estimation of () from a sample of random points inside and outside . The sample design assumes that, for each sample point, we know (without error) whether or not that point belongs to . Under this design we...

Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process

Eva Löcherbach, Dasha Loukianova, Oleg Loukianov (2011)

ESAIM: Probability and Statistics

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Let be a one dimensional positive recurrent diffusion continuously observed on [0,] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when → ∞. The main point of our work is that we do not suppose the process...

Adaptive estimation of the stationary density of discrete and continuous time mixing processes

Fabienne Comte, Florence Merlevède (2010)

ESAIM: Probability and Statistics

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In this paper, we study the problem of non parametric estimation of the stationary marginal density of an or a -mixing process, observed either in continuous time or in discrete time. We present an unified framework allowing to deal with many different cases. We consider a collection of finite dimensional linear regular spaces. We estimate using a projection estimator built on a data driven selected linear space among the collection. This data driven choice is performed the minimization...

On the Average Case Complexity of Some P-complete Problems

Maria Serna, Fatos Xhafa (2010)

RAIRO - Theoretical Informatics and Applications

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We show that some classical P-complete problems can be solved efficiently in NC. The probabilistic model we consider is the sample space of input descriptions of the problem with the underlying distribution being the uniform one. We present parallel algorithms that use a polynomial number of processors and have expected time upper bounded by ( ln 4 + (1))log , asymptotically with high probability, where is the instance size.