Mathematical Statistics Seminar

An Adaptive Composite Quantile Approach to Dimension Reduction for censored data

Speaker(s): 
Efang Kong (University of Kent)
Date: 
Wednesday, November 5, 2014 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Sufficient dimension reduction [Li (1991)] has long been a prominent issue in multivariate nonparametric regression analysis. In this paper, we study dimension reduction (DR) for censored data, where semi-parametric structures are assumed for both the dependent variable and the censoring variable. Incorporating the idea of "redistribution-of-mass'' (Efron, 1967; Portnoy, 2003) for dealing with random censoring, we propose an adaptive composite quantile approach.

Panel Data Models with Interactive Fixed Effects and Multiple Structural

Speaker(s): 
Degui Li (York)
Date: 
Wednesday, October 29, 2014 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

In this paper we consider estimation and inference of common structural breaks in panel data models with interactive fixed effects which are unobservable. We introduce a penalized principal component estimation procedure via adaptive group fused LASSO to detect the multiple structural breaks. Under mild conditions, we show that with probability tending to one our method can correctly determine the unknown number of breaks and consistently estimate the common break dates.

Detecting Relevant Changes in Time Series Models

Speaker(s): 
Dominik Wied (TU Dortmund)
Date: 
Wednesday, October 22, 2014 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Most of the literature on change-point analysis by means of hypothesis testing considers null hypotheses in which a certain parameter is constant over time. This presentation takes a different perspective and investigate the null hypotheses of no relevant changes. Here, the difference between the parameter before and after a change point is smaller than a positive threshold.

Confidence intervals using the graphical Lasso

Speaker(s): 
Sara van de Geer (ETH Zürich)
Date: 
Wednesday, July 2, 2014 - 10:00am
Location: 
Mohrenstraße 39, Erhard-Schmidt-Hörsaal

Over the recent years much statistical theory and methodology for high-dimensional problems has been developed. However, the question of statistical inference in the sense of testing and confidence intervals is less well addressed. In this talk, we consider data consisting of i.i.d. copies a high-dimensional vector X. The aim is to estimate the precision matrix (the inverse of the covariance matrix of X). We use the graphical Lasso as initial estimator and then ”de-sparsify” it. Under certain (sparsity) conditions the entries of this new estimator are asymptotically normal.

Adaptive Rates for Support Vector Machines

Speaker(s): 
Mona Eberts (Stuttgart)
Date: 
Wednesday, June 25, 2014 - 10:00am
Location: 
Mohrenstraße 39, Erhard-Schmidt-Hörsaal

Support vector machines (SVMs) using Gaussian kernels are one of the standard and state- of-the-art learning algorithms. For such SVMs applied to least squares regression we establish new oracle inequalities. With the help of these oracle inequalities, we derive learning rates that are (essentially) minmax optimal under standard smoothness assumptions on the target function. We further utilize the oracle inequalities to show that the achieved learning rates can be adaptively obtained by a simple data- dependent parameter selection method.

Adaptation to lowest density regions with application to support recovery

Speaker(s): 
Piotr Kokoschka (Colorado State University)
Date: 
Wednesday, June 18, 2014 - 10:00am
Location: 
Mohrenstraße 39, Erhard-Schmidt-Hörsaal

A new scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a Hölder continuous density, this locally minimax-optimal bandwidth is shown to be smaller than the usual rate, even in case of homogeneous smoothness.

Lecture series on linear and nonparametric models in functional data analysis

Speaker(s): 
Alexander Meister (Rostock University)
Date: 
Wednesday, June 11, 2014 - 3:00pm to Friday, June 13, 2014 - 12:30pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin

We start with an introduction to the eld of functional data analysis. Then we study nonparametric regression with functional covariates where the theoretical framework allows us to generalize these findings to data from a Polish metric space with specic conditions on the metric entropy. We derive the optimal convergence rates for a  nonparametric estimator of the regression mapping. Also we show that the same minimax rates occur in classication of functional data based on training samples.

Regime Switching Model with Endogenous Autoregressive Latent Factor

Speaker(s): 
Yoosoon Chang (Indiana)
Date: 
Wednesday, June 11, 2014 - 10:00am
Location: 
Mohrenstraße 39, Erhard-Schmidt-Hörsaal

This talk introduces a model with regime switching, which is driven by an autoregressive latent factor correlated with the innovation to the observed time series. In our model, the mean or volatility process is switched between two regimes, depending upon whether the underlying autoregressive latent factor takes values above or below some threshold level. If the latent factor becomes exogenous, our model reduces to the conventional markov switching model, and therefore, our model may be regarded as an extended markov switching model allowing for endogeneity in regime switching.

What Drives the Yield Curve?

Speaker(s): 
Dennis Kristensen (UCL)
Date: 
Wednesday, June 4, 2014 - 10:00am
Location: 
Mohrenstraße 39, Erhard-Schmidt-Hörsaal

We develop nonparametric tests for term structure dynamics to be driven by a nite number of Markov factors in a continuous-time setting. The tests are based on nonparametric estimators of the model developed under the null of the Markov hypothesis and under the alternative, respectively. We then reject the null if the estimators are statistically dierent from each other. The tests do not rely on particular functional form assumptions and so are able to disentangle the Markov hypothesis from functional form hypotheses.

On bandwidth selection in empirical risk minimization

Speaker(s): 
Michael Chichignoud (ETH Zürich)
Date: 
Wednesday, May 28, 2014 - 10:00am
Location: 
Mohrenstraße 39, Erhard-Schmidt-Hörsaal

The well-known Goldenshluger-Lepski method (GLM) allows to select multi-dimensional bandwidths (possibly anisotropic) of kernel estimators and provides optimal results in this setting. However, GLM requires some linearity property, which is not satisfied in empirical risk minimization (where a bandwidth is involved in the empirical risk).

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