Research Seminars

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.

On portfolio optimization under small fixed transaction costs

Speaker(s): 
Jan Kallsen (Christian-Albrechts-Universität zu Kiel)
Date: 
Thursday, November 17, 2016 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

While optimal investment under proportional transaction costs is quite well understood by now, less has been done in the presence of fixed fees for any single transaction. In this talk we consider the asymptotics of the no-trade region for small fixed costs. More specifically, we sketch the rigorous verification for a general univariate Ito process market under exponential utility. (The talk is based on joint work with Mark Feodoria.)

Strong rate of convergence for the Euler-Maruyama approximation of SDES with irregular drift coefficient

Speaker(s): 
Olivier Pamen (University of Liverpool/AIMS Ghana)
Date: 
Thursday, November 17, 2016 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

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.

Model risk of contingent claims

Speaker(s): 
Natalie Packham (Hochschule für Wirtschaft und Recht Berlin)
Date: 
Thursday, October 20, 2016 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

Paralleling regulatory developments, we devise value-at-risk and expected shortfall type risk measures for the potential losses arising from using misspecified models when pricing and hedging contingent claims. Essentially, P&L from model risk corresponds to P&L realized on a perfectly hedged position. Model uncertainty is expressed by a set of pricing models, each of which represents alternative asset price dynamics to the model used for pricing. P&L from model risk is determined relative to each of these models.

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.

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