Displaying similar documents to “Detecting abrupt changes in random fields”

Model selection for (auto-)regression with dependent data

Yannick Baraud, F. Comte, G. Viennet (2001)

ESAIM: Probability and Statistics

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In this paper, we study the problem of non parametric estimation of an unknown regression function from dependent data with sub-gaussian errors. As a particular case, we handle the autoregressive framework. For this purpose, we consider a collection of finite dimensional linear spaces (e.g. linear spaces spanned by wavelets or piecewise polynomials on a possibly irregular grid) and we estimate the regression function by a least-squares estimator built on a data driven selected linear...

Accelerated Monte Carlo estimation of exceedance probabilities under monotonicity constraints

Nicolas Bousquet (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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The problem of estimating the probability p = P ( g ( X ) ≤ 0 ) is considered when X represents a multivariate stochastic input of a monotonic function g . First, a heuristic method to bound p , originally proposed by de Rocquigny (2009), is formally described, involving a specialized design of numerical experiments. Then a statistical estimation of p is considered based on a sequential stochastic exploration of the input space. A maximum likelihood estimator of p build from successive dependent Bernoulli...

Semiparametric deconvolution with unknown noise variance

Catherine Matias (2002)

ESAIM: Probability and Statistics

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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...

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

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We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U -statistics of order 2 due to Houdré and Reynaud.