Research Group "Stochastic Algorithms and Nonparametric Statistics"

13.10.15

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20.10.15

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27.10.15

03.11.15

10.11.15

Abstract:From an analysis of the time series of realized variance (RV) using recent high frequency data, Gatheral, Jaisson and Rosenbaum (2014) previously showed that log-RV behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. The resulting Rough Fractional Stochastic Volatility (RFSV) model is remarkably consistent with financial time series data. We now show how the RFSV model can be used to price claims on both the underlying and integrated variance. We analyze in detail a simple case of this model, the rBergomi model. In particular, we find that the rBergomi model fits the SPX volatility markedly better than conventional Markovian stochastic volatility models, and with fewer parameters. Finally, we show that actual SPX variance swap curves seem to be consistent with model forecasts, with particular dramatic examples from the weekend of the collapse of Lehman Brothers and the Flash Crash.

17.11.15

Abstract: We review known results and provide some new findings on the sphere covering problem. The motivation for this work is an optimal stopping problem in financial mathematics.

24.11.15

Abstract:In this talk I will introduce data acquisition techniques and properties used in the analysis of functional connectivity. Specifically, I will give an introduction to functional MRI and functional connectivity. I will present how this technique can be potentially used to analyze the dynamics of learning processes.

01.12.15

Andzhey Kozyuk (WIAS Berlin)

Abstract:Inverse problems associated with instrumental variables regression are of interest for applied econometricians (cf. Horowitz). We explain important milestones for applied research in such problems, like "weakness" of instrumental variables or model misspecification. We also discuss a method for estimating a target parameter which allows to address such problems. Under a finite sample assumption and accounting for possible model misspecification we achieve a feasible answer coupling finite sample theory [1] with a multiplier bootstrap technique developed earlier [2]. [1] Spokoiny V. Bernstein-von Mises Theorem for growing parameter dimension //arXiv preprint arXiv:1302.3430. [2] Spokoiny V., Zhilova M. Bootstrap confidence sets under a model misspecification //arXiv preprint arXiv:1410.0347.

09.06.15

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15.12.15

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05.01.16

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12.01.16

Abstract: In statistical inference it is of fundamental importance to obtain the sampling distribution of statistics. However, we often encounter situations where the exact distribution cannot be obtained in closed form, or even if it is obtained, it might be of little use because of its complexity. One practical way of getting around the problem is to provide reasonable approximations of the distribution function and its quantiles, along with extra information on their possible errors. It can be made with help of Edgeworth and Cornish%G–%@Fisher expansions (EE and CFE resp.) (see, e.g., Ulyanov V.V., Cornish-Fisher Expansions, International Encyclopedia of Statistical Science (Ed. M.Lovric), Springer-Verlag, Berlin%G–%@Heidelberg, 2011, p.312%G–%@315). Starting from 90-s the interest for CFE stirred up because of intensive study of risk measures (Value at Risk, Expected Shortfall etc.) In the talk we discuss new approaches to CFE appeared in last years, in particular generalized CFE and rearrangements to monotonize CFE. Generalized CFE (non-normal limit distributions) appear naturally for statistics based on samples of random size. We consider as well the computable error bounds for CFE in the case when there are error bounds for EE of the distributions of statistics. The different applications for risk measurement and construction of the confidence intervals will be also discussed.

19.01.16

Abstract: In this work bootstrap analogue of log-likelihood ratio test is constructed and justified to recover real world log-likelihood ratio test statistic under finite sample assumption and possibly misspecified model. This procedure is further used to test hypothesis in two linear equations model with hypothesis formed on associated with instrumental variables (IV) parameters. It is numerically demonstrated that the test's power for both weak and strong IV identification is comparable to existing tests in literature.

26.01.16

Abstract:Multiview geometry is a natural extension of epipolar geometry to more than two cameras. Here 3D points are projected by n cameras A_i in R^{3 x4} onto n 2D images. In this talk I give a short introduction to some algebraic ideas in mulitview geometry. There are certain algebraic relations between the 2d images, which define the so called "multiview variety". Knowledge about the multiview variety can be used to reduce noise in the images. We then turn our attention to the case of images of two rigid points. Here we derive additional relations between the images and give a set-theoretical description of this variety. The last part of the talk is based on joint work with Michael Joswig, Joe Kileel and Bernd Sturmfels.

02.02.16

Egor Klochkov (Humboldt-Universität zu Berlin)

Sieve maximum likelihood estimation in semi-parametric regression with errors in variables

Abstract:We consider error-in-variables regression models with unknown distribution of the errors. We parameterize the problem by sieve approximations and consider semiparametric maximum likelihood estimator. The performance of the estimator is studied under certain conditions on the design. This is a joint work with Denis Belomestny and Vladimir Spokoiny.

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02.02.16

Egor Klochkov (Humboldt-Universität zu Berlin)

Sieve maximum likelihood estimation in semi-parametric regression with errors in variables

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01.03.16

Valeriy Avanesov (WIAS Berlin)

Consistency results and confidence intervals for adaptive l1-penalized estimators of the high-dimensional sparse precision matrix

Abstract:In this talk we present our recent results on l1-penalized estimators for the precision matrix in a finite-sample setting. We present consistency results and construct confidence intervals for the elements of the true precision matrix. The application to the estimation of functional connectivity networks in functional Magnetic Resonance data and the elaboration of the theoretical results in extensive simulation experiments will be presented as well.

15.03.16

Dr. Christian Bayer (WIAS Berlin)

Rough paths and rough partial differential equations (Part I)

Abstract: We give an introduction to Terry Lyons' theory of rough paths. We study the construction of solutions of rough (ordinary) differential equations in some details. In the end, we also give some hints about the construction of solutions of partial differential equations driven by rough paths.

18.03.16

Dr. Christian Bayer (WIAS Berlin)

Rough paths and rough partial differential equations (Part II)

Abstract: We give an introduction to Terry Lyons' theory of rough paths. We study the construction of solutions of rough (ordinary) differential equations in some details. In the end, we also give some hints about the construction of solutions of partial differential equations driven by rough paths.