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 Objectifs
This course treats in a bi-yearly alternating fashion, some special topics in mathematical
statistics which are not treated by other courses. It is focused around two complimentary
parts: functional estimation, and spectral analysis.
Cahier des charges
The "functional estimation'' part of this course aims at introducing the students to the
various aspects of local modelling in nonparametric and semi-parametric functional
estimation. In this part you will learn about how to develop estimation (or testing)
procedures via local modelling ideas, about theoretical aspects of these procedures
(convergence, asymptotic laws, etc), and about their practical aspects (implementation,
etc). Each year we will focus on two or three related subjects that deal with functional
estimation using local modelling ideas.
The "spectral analysis" part of this course aims at giving students interested in qualitative
signal processing an introduction into the theory and practice of Fourier and local Fourier
(wavelet) analysis. You will learn how to nonparametrically model and analyse statistical
signals (including time series) in the frequency and in the time-frequency domain.
Résumé
CONTENT
PART I: « Functional estimation » :
1. Introduction to local modelling
2. Multivariate (generalized) additive regression models (for example)
3. Modelling interactions (for example)
4. Single-index models (for example)
PART II: « Spectral analysis » :
1. Introduction to Fourier analysis
2. Spectral analysis of time series
3. Time-frequency methods (local Fourier, wavelets, etc.)
4. Spectral representations of stationary and non-stationary processe
Autres informations du cahier des charges
Réf : BILLINGSLEY, P. (1961) : Statistical Inference for Markov Process. University of Chicago Press, Chicago.KARR, A.F. (1986) : Point Process and their Statistical Inference. Marcel Dekker, New York.LIPSTER, R.S. and A.N. SHIRYAYEV (1977) : Statistics of Random Processes. Springer-Verlag, New York.BASAWA, I. and B.L.S. PRAKASA RAO (1980) : Statistical Inference for Stochastic Processes. Academic Press, London.
Le cours STAT3130 est mentionné dans les programmes suivants :
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STAT3DA
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Diplôme d'études approfondies en statistique
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Valeurs ECTS de l'activité
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STAT3DA/E
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diplôme d'études approfondies en statistique (statistique et économétrie)
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(3 ECTS)
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STAT3DA/M
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Diplôme d'études approfondies en statistique (méthodologie de la statistique)
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(3 ECTS)
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STAT3DA/P
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diplôme d'études approfondies en statistique (pratique de la statistique)
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(3 ECTS)
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Valeur ECTS par défaut
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(3 ECTS)
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