H2020Индивидуална стипендия2015–2017

ResMet · Resampling methods for nonstationary stochastic processes

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2015-10-01 → 2017-09-30
Финансиране от ЕС: 173 076 €
Участници: 1
Схема: MSCA-IF-EF-ST

Линиите свързват координатора с партньорите.

Накратко на български

Методите за повторно вземане на проби анализират данни с периодични структури, като например колебания в климата или виброакустични сигнали. Те помагат за по-точното изчисляване на характеристиките на тези процеси, дори когато данните са кратки, разпръснати или с променлив период.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Resampling methods for nonstationary stochastic processes

My project was dedicated to applications of resampling methods in statistical inference for the processes with periodic and almost periodic structures. The mentioned processes in the literature are called cyclostationary (CS) and almost cyclostationary (ACS). Studies of CS/ACS processes started by Gladyshev in 1961. Since then the subject has developed fast and found applications in many branches of vibroacoustics, mechanics, signal analysis and climatology. The wide range of possible applications resulted in the thousands of papers that were published through the last 60 years. Unfortunately, the analysis of CS/ACS processes is very difficult and many problems are still unsolved. My objective was to provide tools for practitioners that will help them: • to deal with short samples from periodic data, to construct confidence intervals for time and frequency characteristics of CS and ACS processes; • to test significance of particular frequencies and hence be sure that the mean function was correctly removed from the data; • to analyze data in the presence of jitter effect i.e., in the situation when time instances in which the considered process is observed are disturbed; • to analyze data randomly sampled i.e., data for which times between the consecutive observations are not always equally spaced; • to deal with data with non-zero mean function; • to analyze data for which period is changing in time; • to choose suitable for the considered problem bootstrap technique. The obtained results can be applied in any setting, where data with periodic or almost periodic structure appear e.g., in economics, vibroacoustics, mechanics, signal processing, medicine, hydrology, climatology. My additional objective was to make French habilitation, which will allow me to get professor position, supervise PhD students and create my own research group.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

ResMet is dedicated to applications of resampling methods in statistical inference for the processes with periodic and almost periodic structures. The mentioned processes in the literature are called cyclostationary (CS) and almost cyclostationary (ACS). Studies of CS/ACS processes started by Gladyshev in 1961. Since then the subject has developed fast and found applications in many branches of vibroacoustics, mechanics, signal analysis and climatology. The wide range of possible applications resulted in the thousands of papers that were published through the last 60 years. Unfortunately, the analysis of CS/ACS processes is very difficult. The most difficult is the estimation of the asymptotic covariance matrix for parameters of interest. In practice it is almost impossible and to construct confidence intervals resampling methods need to be used. The Experienced Researcher (ER) will show their consistency for different parameters of CS/ACS processes. Additionally, she will consider jitter effect and develop testing tools to detect the significant frequencies and to check if the considered data are zero-mean. These results will allow e.g. for construction of the new tools for machine faults detection. Moreover, new research topics will appear like choosing the optimal block length for each application. During the fellowship the ER will be able to work with the experts (her supervisor Prof. Dehay included) in the analysis of AC/ACS processes and in testing. The ER will join the seminars organized by them and will exchange the knowledge on the daily basis with other statisticians. Finally, she will present results of her work on the seminars, workshops and conferences. This process will allow her to finish her habilitation and apply for the permanent professor position in Europe. Moreover, during her secondment at Laser Analytica she will get statistical consulting experience, which in future will allow her for collaboration with pharmaceutical companies in Europe.

Оригинален текст от CORDIS (на английски).

Участници

UNIVERSITE RENNES II · Rennes CedexКоординаторФранция