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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 via the minimization...
In this paper, we study the problem of non parametric estimation
of the stationary marginal density f of an α or a
β-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 f using a
projection estimator built on a data driven selected linear space
among the collection. This data driven choice is performed via the
minimization...
In a convolution model, we observe random variables whose distribution is the convolution of some unknown density f and some known noise density g. We assume that g is polynomially smooth. We provide goodness-of-fit testing procedures for the test H0: f=f0, where the alternative H1is expressed with respect to -norm (i.e. has the form ). Our procedure is adaptive with respect to the unknown smoothness parameterτ of f. Different testing rates (ψn) are obtained according to whether f0 is polynomially...
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. These filter methods are generally restricted to monotonic transformations, e.g. the Tikhonov regularization or the spectral cut-off. However, in several cases, non-monotonic sequences of filters may appear more appropriate. In this paper, we study a hard-thresholding regularization method that extends the spectral cut-off procedure to non-monotonic sequences....
We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.
We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.
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...
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 derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent robust...
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...
An accuracy of parameter estimates need not be sufficient for their unforeseen utilization. Therefore some additional measurement is necessary in order to attain the required precision. The problem is to express the correction to the original estimates in an explicit form.
Gaussian Process models are often used for predicting and approximating expensive experiments. However, the number of observations required for building such models may become unrealistic when the input dimension increases. In oder to avoid the curse of dimensionality, a popular approach in multivariate smoothing is to make simplifying assumptions like additivity. The ambition of the present work is to give an insight into a family of covariance kernels that allows combining the features of Gaussian...
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