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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...
We propose a test of a qualitative hypothesis on the mean of a -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 which are related to Hölderian balls in functional spaces. We provide a simulation study in order...
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 which are
related to Hölderian balls in functional
spaces. We provide a simulation study in...
In this paper, we firstly introduce a recursive kernel estimator of the density in the censored data case. Then, we establish its pointwise and uniform almost complete convergences, with rates, in both complete and censored independent data. Finally, we illustrate the accuracy of the proposed estimators throughout a simulation study.
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 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 and under local alternatives with a QTL at on . We show that the LRT process is asymptotically...
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...
An approximation error and an asymptotic formula are given for shift invariant operators of polynomial order ϱ. Density estimators based on shift invariant operators are introduced and AMISE is calculated.
The P.O.T. (Peaks-Over-Threshold) approach consists of using the Generalized Pareto Distribution (GPD) to approximate the distribution of excesses over a threshold. We use the probability-weighted moments to estimate the parameters of the approximating distribution. We study the asymptotic behaviour of these estimators (in particular their asymptotic bias) and also the functional bias of the GPD as an estimate of the distribution function of the excesses. We adapt penultimate approximation results...
The P.O.T. (Peaks-Over-Threshold) approach
consists of using the Generalized Pareto Distribution (GPD)
to approximate the distribution of excesses over a threshold.
We use the probability-weighted moments
to estimate the parameters of the approximating distribution.
We study the asymptotic behaviour of
these estimators (in particular their asymptotic bias) and also the
functional bias of the GPD as an estimate of the
distribution function of the excesses. We adapt penultimate
approximation results...
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and...
In this paper we consider a kernel estimator of a density in a convolution model and give a central limit theorem for its integrated square error (ISE). The kernel estimator is rather classical in minimax theory when the underlying density is recovered from noisy observations. The kernel is fixed and depends heavily on the distribution of the noise, supposed entirely known. The bandwidth is not fixed, the results hold for any sequence of bandwidths decreasing to 0. In particular the central limit...
We build a kernel estimator of the Markovian transition operator as an endomorphism on L¹ for some discrete time continuous states Markov processes which satisfy certain additional regularity conditions. The main result deals with the asymptotic normality of the kernel estimator constructed.
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