Mathematical Statistics Seminar

Network dynamics of high-frequency trading data: Evidence from NASDAQ market

Speaker(s): 
Shi Chen (HU Berlin, IRTG 1792)
Date: 
Wednesday, November 23, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We propose a robust connectedness estimator for limit order books in high dimensional setting, and we argue that limit orders have significant market impacts. The estimator is constructed based on sparse precision matrix using graphical lasso, so that the regularized covariance matrix is related to connectedness measure. The microstructure noise embedded in high frequency data is removed by pre-averaging estimation. Furthermore, we provide a jump-robust estimator for connectedness of NASDAQ firms from different industrial sectors.

Statistical properties of Bernstein copulae with applications in multiple testing

Speaker(s): 
Thorsten Dickhaus (Universität Bremen)
Date: 
Wednesday, November 16, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

A general way to estimate continuous functions consists of approximations by means of Bernstein polynomials. Sancetta and Satchell (2004) proposed to apply this technique to the problem of approximating copula functions. The resulting so-called Bernstein copulae are nonparametric copula estimates with some desirable mathematical features like smoothness. We extend previous statistical results regarding bivariate Bernstein copulae to the multivariate case and study their impact on multiple tests.

Asymptotic equivalence between density estimation and the Gaussian white noise model revisited

Speaker(s): 
Johannes Schmidt-Hieber (Universität Leiden)
Date: 
Wednesday, November 9, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Asymptotic equivalence means that two statistical models have the same asymptotic properties with respect to all decision problems with bounded loss. In nonparametric statistics, asymptotic equivalence has been found useful as it allows in some situations to switch to simpler models. One of the most famous results is Nussbaums theorem which states that nonparametric density estimation is asymptotically equivalent to a Gaussian shift model provided that the densities satisfy some smoothness assumptions and are bounded away from zero.

Network models and sparse graphon estimation

Speaker(s): 
Olga Klopp (Université Paris-Quest Nanterre)
Date: 
Wednesday, November 2, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical estimation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network and derive optimal rates of convergence for this problem. Our results cover the important setting of sparse networks. We also establish upper bounds on the mini-max risk for graphon estimation when the probability matrix is sampled according to a graphon model.

Uncertainty quantification through adaptive and honest confidence sets

Speaker(s): 
Alexandra Carpentier (Universität Potsdam)
Date: 
Wednesday, October 26, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Empirical uncertainty quantification of estimation procedures can be simple in parametric, low dimensional situations. However, it becomes challenging and often problematic in high and in finite dimensional models. Indeed, adaptivity to the unknown model complexity becomes key in this case, and uncertainty quantification becomes akin to model estimation.
- Such model-adaptive uncertainty quantification can be formalised through the concept of adaptive and honest confidence sets. Recent results related to this concept will be presented.

Statistical Learning of Dynamic Systems

Speaker(s): 
Itai Dattner (University of Haifa)
Date: 
Wednesday, October 19, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Dynamic systems are ubiquitous in nature and are used to model many processes in biology, chemistry, physics, medicine, and engineering. In particular, systems of (deterministic or stochastic) differential equations are commonly used for the mathematical modeling of the rate of change of dynamic processes. These systems describe the interrelationships between the variables involved, and depend in a complicated way on unknown quantities (e.g., initial values, constants or time dependent parameters).

Beyond stochastic gradient descent for large-scale machine learning

Speaker(s): 
Francis Bach (INRIA Paris)
Date: 
Wednesday, July 20, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Many machine learning and statistics problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations (''large n'') and each of these is large (''large p''). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes over the data.

Non-asymptotic analysis – general approach

Speaker(s): 
Vladimir V. Ulyanov (Lomonosov Moscow State University)
Date: 
Wednesday, July 13, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

First we give short review on recent approximation results for non-linear forms in independent random elements including asymptotic expansions. The errors of approximations could be described either in asymptotic way as an order of a remainder term with respect to number $n$ of random elements or in non-asymptotic form as a bound for remainder term with explicitly written dependence on $n$, moment characteristics and dimension $p$ of random elements or observations .

Nonparametric statistical tests using kernels

Speaker(s): 
Arthur Gretton (UCL)
Date: 
Wednesday, July 6, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

I will describe a kernel approach to hypothesis testing, based on a representation of probability distributions in a reproducing kernel Hilbert space. I will first derive a metric as the distance between these representations. Next, I will describe both tests of homogeneity (of whether two samples are from the same distribution), and of independence (of whether a joint distribution factorises into a product of marginals).

CANCELLED: Stochastic optimization and high-dimensional sampling

Speaker(s): 
Eric Moulines (Ecole Polytechnique, France)
Date: 
Wednesday, June 29, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Recently, the problem of designing MCMC samplers adapted to high-dimensional Bayesian inference with sensible theoretical guarantees has received a lot of interest. The applications are numerous, including large-scale inference in machine learning, Bayesian nonparametrics, Bayesian inverse problem, aggregation of experts among others.

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