Semester projects offered by members of the Chair of Statistics




A list of past projects you find here.


Title Level Responsible
Monetary Systems STS C.D. Osinski
Metropolis-Hastings Algorithms for Penalised Profile Likelihood MA 2e cycle M-O. Boldi
Volatility Structure of Stock Prices MA 2e cycle C.D. Osinski
Image Denoising using Wavelets SSC or DI 2e cycle S. Sardy
Estimating the smoothing parameter in wavelet denoising DMA 2e cycle S. Sardy



  • Monetary Systems

    This STS project intends to give an overview of the monetary systems adopted by our governments. The topics that may be tackled are:
    • origins and evolution of currencies;
    • emission of currency by the governments;
    • the mains rules of a monetary policy;
    • the exchange and interest rates (how are they set?);
    • the mathematical models for exchange and interest rates.
    The different topics may be treated separately by different students.

    Requirements: motivation

    For further information, please contact Christophe D. Osinski.

    Added on Friday, 01 March 2002


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  • Metropolis-Hastings Algorithms for Penalised Profile Likelihood

    In the framework of penalised likelihood based inference, the interpretation of the penalty as a prior density provides a good justification for the use of bayesian techniques. However improper priors are still questionable and lots of statiticians reject them. This project aims to adapt Metropolis-Hastings algorithms in the case of the presence of a nuisance parametre avoiding improper prior. This project will certainely require fairely good skills in S-Plus coding, but, as it is a wide subject, previous statiscal requirements can be adapted. However it should be more interesting for someone who has already attended the Monte-Carlo Inference course (or equivalent).

    Requirements: motivation

    For further information, please contact Marc-Olivier Boldi.

    Added on Friday, 19 October 2001


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  • Volatility Structure of Stock Prices

    In recent years many discrete time models have been developed to fit financial data. Among the most popular are the ARCH family. One of the last arrived in this family is the HARCH process. This process has many nice proprieties like considering different levels in the volatility depending on the time horizon of the investors.

    The project would consist in learning about ARCH type processes, especially HARCH and fitting those models to stock returns. Two interesting questions then appear, the first one for ARCH type processes in general and the second for the HARCH process:
    • what is the quality of the fit?
    • which kind of investor (short, middle, long-term) operates on the NASDAQ, SMI, S&P500,...?

    Requirements: knowledge in time series

    For further information, please contact Christophe D. Osinski.

    Keywords: log-returns; volatility; t-distribution; auto-correlation; cross-correlation; ARCH models

    Added on Thursday, 11 January 2001


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  • Image Denoising using Wavelets

    Generalized Basis Pursuit, a recent denoising technique to denoise image, involves solving an optimization problem. The technique is currently using an interior point algorithm. The technique has already been programed in Matlab but is slow for large images. The project would consist in programing the same technique in a faster language like C or C++.

    Requirements: good programming skills, some mathematics, interest in image processing, motivation

    If you want further information, please contact Sylvain Sardy.

    Added on Wednesday, 3 May 2000


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  • Estimating the smoothing parameter in wavelet denoising

    To estimate a noisy signal with WaveShrink (a wavelet-based non-parametric estimator) a crucial step is the selection of the smoothing parameter. Many techniques have been developped amoung which minimax, cross validation and SURE. I have a fairly simple idea that looks promissing based on the simulations I made. If you want to do some mathematical derivations to develop this new technique and do some computer simulations to see how it works in practice, let me know.

    Requirements: interest in the area of smoothing (function estimation from noisy data); programming skills; basic knowledge of statistics; motivation.

    If you want further information, please contact Sylvain Sardy.

    Added on Tuesday, 18 January 2000


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This page is maintained by Christophe D. Osinski, Christophe.Osinski@epfl.ch.
Last modified: Thu Mar 14 18:22:21 MET 2002