corso: inferenza per processi

[Valentina Leucari <vl@dimat.unipv.it>]

A tutti gli interessati:



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Dottorato di ricerca in Matematica e Statistica
Universitā degli Studi di Pavia
Dipartimento di Matematica F.Casorati
via Ferrata 1, Pavia


Si comunica che il 
Prof. Ildar Ibragimov (Laboratory of Statistical Methods Steklov Institute
of Mathematics
St. Petersburg, Russia) terrā un  corso (in inglese) su

                        Statistica dei Processi Stocastici


Il corso si svolgerā presso il Dipartimento di Matematica via Ferrata 1, Pavia
a partire dal 19 Novembre 2001, per la durata di un mese. L'orario č ancora
da definire. 

La partecipazione č libera ma si prega di darne conferma prima dell'inizio
del corso  a

Federico Bassetti, bassetti@dimat.unipv.it 
oppure
Valentina Leucari, vl@dimat.unipv.it

Ulteriori informazioni saranno rese disponibili, appena possibile, sul sito 

http://dimat.unipv.it/~statprob/welcome.htm

Si allega di seguito il programma.

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                              I. IBRAGIMOV
                STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES

This course presents an outline of the theory of statistical inference
in stochastic processes in author's understanding of the subject.
Namely the author thinks that despite that the statistical methods
of investigation are general their concrete application heavely
depend on a process under consideration. Because of this the
structure of the course repeats the structure of classic books
on stochastic processes.
 
1. Introduction. Statistical problems arising in connection with
stochastic processes. Observables. Classification of statistical problems.
Examples:Wiener process, point processes, diffusion processes,
semimartingales,
stationary processes, spatial processes etc. Parametric and nonparametric
problems.

 2. Statistical background. General sstatistical notions in connection
with stochastic processes. Likelihood ratio for stochastic processes.
Methods of its calculation. Asymptotic problems and some general
methods of their investigation. Local asymptotic normality. Parametric
and nonparametric problems.

 3. Lineare inference (=second moment theory). Infinite dimensional
variants of Gauss-Markov least square theory. Grenander theorem.
Examples. Estimation of the mean valuees of stationary processes.
Asymptotic optimality of linear methods.

 4. Inference for Gaussian processes. Hajek-Feldman theorem.
Testing of mean value functions and covariance functions. Examples:
Baxter's theorem, stationary processes with rational spectrum.
Parameter estimation for stationary Gaussian processes.

 5. Inference for time-discrete Markov processes: estimation,
hypotheses testing. Processes with finite number of states.

 6. Markov processes with continuos time and countable
number of states. Birth and death processes.

 7. Inference for diffusion processes. Parametric inference for
diffusion processes: methods for the estimation of the drift
parameter; estimation of the diffusion parameter. Nonparametric
inference for diffusion processes:signal in the Gaussian
white noise; estimation of the drift; estimation of the diffusion
coefficient; examples.

 8. Nonparametric inference for stationary processes: spectral
density estimation, confidence band for spectral functions.