Adaptive tests for periodic signal detection with applications to laser vibrometry
| Autor: | Céline Lévy-Leduc, Magalie Fromont |
|---|---|
| Přispěvatelé: | Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Laboratoire de statistique, Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) |
| Jazyk: | angličtina |
| Rok vydání: | 2006 |
| Předmět: |
Statistics and Probability
Mathematical optimization Logarithm Gaussian 62G10 62G08 62G20 01 natural sciences Signal 010104 statistics & probability symbols.namesake [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] 0502 economics and business Detection theory [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST] 0101 mathematics minimax separation rates 050205 econometrics Mathematics Noise (signal processing) 05 social sciences [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Minimax [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH] Sobolev space Periodic function adaptive test nonparametric regression symbols periodic signal detection Algorithm |
| Zdroj: | ESAIM: Probability and Statistics ESAIM: Probability and Statistics, EDP Sciences, 2006, 10, pp.46-75. ⟨10.1051/ps:1006002⟩ ESAIM: Probability and Statistics, 2006, 10, pp.46-75. ⟨10.1051/ps:1006002⟩ ESAIM: Probability and Statistics, EDP Sciences, 2006, 10, pp.46-75. 〈10.1051/ps:1006002〉 |
| ISSN: | 1292-8100 1262-3318 |
| DOI: | 10.1051/ps:1006002⟩ |
| Popis: | 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 l 2-distance between the signal and zero so that the detection is possible with prescribed probabilities of error. Then, we propose a testing procedure which is available when the variance of the noise is unknown and which does not use any prior information about the smoothness degree or the period of the signal. We prove that it is adaptive in the sense that it achieves, up to a possible logarithmic factor, the minimax separation rate over various periodic Sobolev balls simultaneously. The originality of our approach as compared to related works on the topic of signal detection is that our testing procedure is sensitive to the periodicity assumption on the signal. A simulation study is performed in order to evaluate the effect of this prior assumption on the power of the test. We do observe the gains that we could expect from the theory. At last, we turn to the application to target detection by laser vibrometry that we had in view. |
| Databáze: | OpenAIRE |
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