A Conditional Minimax Approach in Survey Sampling.
A minimax property of translation invariant estimators for variance components
Adaptive tests for periodic signal detection with applications to laser vibrometry
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
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...
Admissible and Minimax Estimators of ...r in the Gamma Distribution with Truncated Parameter Space.
An admissible estimator of a lower-bounded scale parameter under squared-log error loss function
Estimation in truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria such as admissibility and minimaxity have to be looked for among others. In this paper we consider a subclass of the exponential families of distributions. Bayes estimator of a lower-bounded scale parameter, under the squared-log error loss function with...
Approximately Optimum Two-Stage Sampling Plans.
Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms
Asymptotically minimax estimation of order-constrained parameters and eigenfunctions of the laplacian on the ball
Change-point estimation from indirect observations. 1. Minimax complexity
We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.
Construction of Minimax-Tests for Bounded Families of Probability-Densities.
Decision making in an incompletely known stochastic system, II
Efficiency rate and local deficiency of the most powerful tests in the model of contaminacy with general neighbourhoods
Error analysis of dynamical models in epidemiology.
Estimating a discrete distribution via histogram selection
Our aim is to estimate the joint distribution of a finite sequence of independent categorical variables. We consider the collection of partitions into dyadic intervals and the associated histograms, and we select from the data the best histogram by minimizing a penalized least-squares criterion. The choice of the collection of partitions is inspired from approximation results due to DeVore and Yu. Our estimator satisfies a nonasymptotic oracle-type inequality and adaptivity properties in the minimax...
Estimating a discrete distribution via histogram selection
Our aim is to estimate the joint distribution of a finite sequence of independent categorical variables. We consider the collection of partitions into dyadic intervals and the associated histograms, and we select from the data the best histogram by minimizing a penalized least-squares criterion. The choice of the collection of partitions is inspired from approximation results due to DeVore and Yu. Our estimator satisfies a nonasymptotic oracle-type inequality and adaptivity properties in the minimax...
Estimation fonctionnelle. Risque minimax
Estimation with delayed observations
Gamma minimax nonparametric estimation
Let Y be a random vector taking its values in a measurable space and let z be a vector-valued function defined on that space. We consider gamma minimax estimation of the unknown expected value p of the random vector z(Y). We assume a weighted squared error loss function.
Gamma-Minimax Estimation of a Multivariate Normal Mean.