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Adaptive tests for periodic signal detection with applications to laser vibrometry

Magalie Fromont, Céline Lévy-leduc (2006)

ESAIM: Probability and Statistics

Initially motivated by a practical issue in target detection via laser vibrometry, we are interested in the problem of periodic signal detection in a Gaussian fixed design regression framework. Assuming that the signal belongs to some periodic Sobolev ball and that the variance of the noise is known, we first consider the problem from a minimax point of view: we evaluate the so-called minimax separation rate which corresponds to the minimal l2-distance between the signal and zero so that the detection...

Adaptive tests of homogeneity for a Poisson process

M. Fromont, B. Laurent, P. Reynaud-Bouret (2011)

Annales de l'I.H.P. Probabilités et statistiques

We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in -norm over classical Besov bodies and weak Besov bodies. Surprisingly, the obtained lower bounds over weak Besov bodies coincide with the minimax estimation rates over such classes. Then we construct non-asymptotic and non-parametric testing procedures that are adaptive in the sense that they achieve, up to a possible logarithmic...

Adaptive tests of qualitative hypotheses

Yannick Baraud, Sylvie Huet, Béatrice Laurent (2003)

ESAIM: Probability and Statistics

We propose a test of a qualitative hypothesis on the mean of a n -gaussian vector. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on the alternative. The properties of the test are non-asymptotic. For testing positivity or monotonicity, we establish separation rates with respect to the euclidean distance, over subsets of ℝ n which are related to Hölderian balls in functional spaces. We provide a simulation study in order...

Adaptive tests of qualitative hypotheses

Yannick Baraud, Sylvie Huet, Béatrice Laurent (2010)

ESAIM: Probability and Statistics

We propose a test of a qualitative hypothesis on the mean of a n-Gaussian vector. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on the alternative. The properties of the test are non-asymptotic. For testing positivity or monotonicity, we establish separation rates with respect to the Euclidean distance, over subsets of ℝ n which are related to Hölderian balls in functional spaces. We provide a simulation study in...

Adaptive wavelet estimation of the diffusion coefficient under additive error measurements

M. Hoffmann, A. Munk, J. Schmidt-Hieber (2012)

Annales de l'I.H.P. Probabilités et statistiques

We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular in high frequency financial data modelling, however mainly from a parametric and semiparametric point of view. This paper addresses the nonparametric estimation of the path of the (possibly stochastic) diffusion coefficient in a relatively general setting. By...

Aligned rank tests in measurement error model

Radim Navrátil, A. K. Md. Ehsanes Saleh (2016)

Applications of Mathematics

Aligned rank tests are introduced in the linear regression model with possible measurement errors. Unknown nuisance parameters are estimated first and then classical rank tests are applied on the residuals. Two situations are discussed: testing about an intercept in the linear regression model considering the slope parameter as nuisance and testing of parallelism of several regression lines, i.e. whether the slope parameters of all lines are equal. Theoretical results are derived and the simulation...

An application of nonprarametric Cox regression model in reliability analysis: a case study

Petr Volf (2004)

Kybernetika

The contribution deals with an application of the nonparametric version of Cox regression model to the analysis and modeling of the failure rate of technical devices. The objective is to recall the method of statistical analysis of such a model, to adapt it to the real–case study, and in such a way to demonstrate the flexibility of the Cox model. The goodness-of-fit of the model is tested, too, with the aid of the graphical test procedure based on generalized residuals.

An approximate necessary condition for the optimal bandwidth selector in kernel density estimation

L. Gajek, A. Lenic (1993)

Applicationes Mathematicae

An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.

An asymptotic test for Quantitative Trait Locus detection in presence of missing genotypes

Charles-Elie Rabier (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [ 0 , T ] representing a chromosome. The originality is in the fact that some genotypes are missing. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [ 0 , T ] and under local alternatives with a QTL at t ☆ on [ 0 , T ] . We show that the LRT process is asymptotically...

An asymptotically unbiased moment estimator of a negative extreme value index

Frederico Caeiro, M. Ivette Gomes (2010)

Discussiones Mathematicae Probability and Statistics

In this paper we consider a new class of consistent semi-parametric estimators of a negative extreme value index, based on the set of the k largest observations. This class of estimators depends on a control or tuning parameter, which enables us to have access to an estimator with a null second-order component of asymptotic bias, and with a rather interesting mean squared error, as a function of k. We study the consistency and asymptotic normality of the proposed estimators. Their finite sample...

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