Research Group "Stochastic Algorithms and Nonparametric Statistics"

Peter Mueller (MD Anderson, Houston, Texas)

Bayesian Approaches to Multiple Testing

Abstract:Many inference problems that arise in biomedical research lead to challenging massive multiple comparisons. Examples include comparison of relative gene expression across biologic conditions, comparison of adverse event rates across a large number of adverse events, subgroup analysis, selection of edges in molecular networks and many more. Popular statistical methods for these problems are often constructed to control false discovery rate (FDR) and similar error summaries. We will discuss similar Bayesian approaches, including posterior expected FDR control, optimal discovery rate and a Bayesian approach to subgroup analysis.

Bojan Basrak (University of Zagreb)

Regularly varying multivariate time series

Abstract:A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional distribution of the rescaled series given that, at a fixed time instant, its distance to the origin exceeds a threshold tending to infinity. The limit object, called the tail process, admits a decomposition in independent radial and angular components. Under an appropriate mixing condition, this tail process allows for a concise and explicit description of the limit of a sequence of point processes recording both the times and the positions of the time series when it is far away from the origin. The theory is applied to multivariate moving averages of finite order with random coefficient matrices.

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Dmitry M. Malioutov (MIT, Boston)

Sparsity in signal processing, finance and machine learning

Abstract:In this talk we venture outside of statistics, and consider applications of sparsity to other disciplines including signal processing, finance, and machine learning. We start with a brief historical overview of 'sparse signal representation', which was at the forefronts of the research on sparsity, and discuss both theory and algorithms of searching for sparse solutions. Next we discuss a few applications of sparsity ranging from source-localization to sparse portolio selection and risk management in equities. Time-permitting we will also discuss a recent approach for sequential discovery of sparse solutions in the compressed sensing setting.

Dominique Picard u. Gerard Kerkyacharian (Paris VII)

Well localized frames, representation of function spaces, and heat kernel estimates

Abstract:Since during the last twenty years, wavelet theory has proved to be a very useful tool for theorical purposes as well as for applications, in this talk, we will revisit and provide an extension of this theory in a general geometric framework. This extension has already been performed for different cases: the interval, the ball, the sphere, and has been extensively used in statistical applications ( for instance in tomography). We will try to show that the construction of wavelets on some spaces is highly related to the geometry of the space and the behavior of the "heat kernel" genuily associated.

Cristina Butucea (Lille)

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Pierre Alquier (Paris 7)

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Marc Hoffmann (ENSAE, Paris)

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Statistical inference and nancial data modelling across time scales

Abstract:On microscopic scales, nancial data derived from order book dynamics such as the last traded price, the best bid or the ask price are point processes. On appropriate scales, these random processes are correctly approximated by Brownian diusions. We will present some multivariate models based on mutually exciting point processes that reproduce some high frequency data stylized facts (such as microstructure noise or the Epps eect) and that converge to Brownian diusions (or the like) on macroscopic scales. In particular, we will be able to trace some microscopic eects (such as the negative correlation of the price increments) that are usually attributed to price manipulation by market makers and give some tentative interpretation of these eects as far as the macroscopic stability of the volatility is concerned. These models as well as their ability to reproduce stylized facts, together with the performances of associated estimators will be confronted to real data examples (mainly xed income ow products). The structure of the underlying statistical experiments will also be discussed from a more theoretical point of view.

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Mathieu Rosenbaum (CREST Paris)

Asymptotic results for time-changed Lévy processes sampled at hitting times

Abstract: We provide asymptotic results for time-changed Lévy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with respect to the starting point is equal to d. This setting can be seen as a first step towards a model for tick-by-tick financial data allowing for large jumps. For a wide class of Lévy processes, we introduce a renormalization depending on d, under which the Lévy process converges in law to an alpha-stable process as d goes to 0. The convergence is extended to moments of hitting times and overshoots. These results can be used to build high frequency statistical procedures. As examples we construct consistent estimators of the time change and, in the case of the CGMY process, of the Blumenthal-Getoor index. Convergence rates and a central limit theorem are established under additional assumptions. This is joint work with Peter Tankov.

Florian Gach (Cambridge)

Efficiency in Indirect Inference

Abstract:Indirect inference is a simulation-based alternative to maximum likelihood estimation when the likelihood function is intractable. The method was introduced in the literature by Smith (1990). The indirect inference estimator proposed there turns out to be consistent and asymptotically normal but is efficient only under the somewhat restrictive assumption that the so-called auxiliary model is correctly specified. In this talk, I give an overview of the method and present a new framework leading to efficient estimation.

On (Semi)-Intrinsic Statistical Analysis of Shape

Abstract:In the statistical analysis of shape, data are considered on non-Euclidean spaces, typically stratications of manifolds. Most research in the past decades applied methods of multivariate Euclidean statistics using local linearizations of these non-linear spaces. In particular, a large number of concepts of mean shape have been proposed. In this talk, under an intrinsic perspective, - we take a unifying approach, - establish the property of \manifold stability" for some of these means in view of a two sample test, and - extend the notion of shape means to geodesic principal components. We provide simulations and applications to forest biometry, and we show how crucial it is to linearize these intrinsic concepts in the \right" manner.