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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...

Admissible invariant estimators in a linear model

Czesław Stępniak (2014)

Kybernetika

Let 𝐲 be observation vector in the usual linear model with expectation 𝐀 β and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic 𝐚 T 𝐲 is called invariant estimator for a parametric function φ = 𝐜 T β if its MSE depends on β only through φ . It is shown that 𝐚 T 𝐲 is admissible invariant for φ , if and only if, it is a BLUE of φ , in the case when φ is estimable with zero variance, and it is of the form k φ ^ , where k 0 , 1 and φ ^ is an arbitrary BLUE, otherwise. This result is used in...

Advanced approach for the public transportation regulation system based on cybercars

Asma Melki, Slim Hammadi, Yves Sallez, Thierry Berger, Christian Tahon (2010)

RAIRO - Operations Research

In the last decade, the authorities require the use of safe, comfortable vehicles to assure a door to door aspect with respect of environment in the urban context. In this paper, we propose an advanced approach of transport regulation where we integrate cybercars into a regulation process as an alternative in disruption cases. For that, we propose an ITS architecture including public transportation and cybercars into the same framework. We will show that collaboration between these two systems...

Algunos progresos y problemas en la Ciencia de la decisión.

Sixto Ríos (1998)

Revista Matemática Complutense

The study of decision making and problem solving has attracted much attention. Since the middle of this century the notion of rational decision making was associated with expected utility maximization, albeit in a very different way than D. Bernoulli (1738) envisioned. For decisions under risk, Von Neumann and Morgenstern (1947) formulated the axioms for expected utility. For decisions under uncertainty Savage (1954) developed the axioms leading simultaneously to subjective probability and expected...

An admissible estimator of a lower-bounded scale parameter under squared-log error loss function

Eisa Mahmoudi, Hojatollah Zakerzadeh (2011)

Kybernetika

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...

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