Research Group "Stochastic Algorithms and Nonparametric Statistics"

no talk!

Abstract:

Dominik Wied (TU Dortmund)

Detecting relevant changes in time series models

Abstract: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. This formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary, if the difference between the parameters before and after the change-point is small. Moreover, the framework allows for constructing confidence intervals. A general approach to problems of this type is developed which is based on the CUSUM principle. For the asymptotic analysis weak convergence of the sequential empirical process has to be established under the alternative of non-stationarity and it is shown that the resulting test statistic is asymptotically normal distributed. Several applications of the methodology are given including tests for relevant changes in the mean, parameter in a linear regression model and distribution function. The finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analyzing a data example from economics.

>Dr. Degui Li (University of York, UK)

Panel data models with interactive fixed effects and multiple structural breaks

Abstract: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. Furthermore, to improve the convergence rates, we estimate the regression coefficients through the post-LASSO method and establish the asymptotic distribution theory of the resulting estimators. We also propose a data-driven method to determine the tuning parameter involved in the penalized principal component estimation procedure. The Monte Carlo simulation results demonstrate that the proposed method works well in finite sample case.

Efang Kong (University of Kent at Canterbury, UK)

An adaptive composite quantile approach to dimension reduction for censored data

Abstract: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. As a general dimension reduction method, it requires minimal assumptions and is capable of recovering the entire DR spaces for both the dependent variable and the censoring variable and based on numerical evidence is more efficient than some existing methods compared with parametric methods such as the Cox proportional hazard (PH) model and the accelerated failure time (AFT) model, our new approach runs less risk of model misspecification, but retains comparable efficiency due to its use of a structure-adaptive kernel function. Asymptotic results are proved and numerical examples are provided. An application of the new method in the study of the popular primary biliary cirrhosis data, leads to a conclusion more consistent with empirical medical evidence than existing statistical analysis did.

Ester Mariucci (Laboratoire Jean Kuntzmann, Grenoble, France) Asymptotic equivalence for discretely or continously observed Lévy processes and Gaussian white noise

Abstract:When looking for asymptotic results for some statistical model it is often useful to dispose of a global asymptotic equivalence, in the Le Cam sense, in order to be allowed to work in a simpler model. In this talk, after giving an introduction to the main characters involved in the Le Cam theory, I will focus on equivalence results for Levy processes. I will discuss global asymptotic equivalences between the experiments generated by the discrete (high frequency) or continuous observation of a path of a Levy process and a Gaussian white noise experiment. I will rst focus on the case in which the considered parameter is the drift function; then the setting will be extended to include the Levy density as an unknown parameter. These approximations are given in the sense of the Le Cam -distance, under smoothness conditions on the unknown drift function and Levy density. All the asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other.

Abstract:

Prof. Ulrike Schneider (Wirtschaftsuniversität Wien)

On distributional properties of Lasso-type estimators noise

Abstract:Penalized least-squares estimators, such as the famous Lasso estimator, have been studied intensively in the statistics literature in the past decade. While many aspects of these estimators are well-understood, still, relatively little is known about their distributional properties, such as nite- and large-sample distributions, uniform convergence rates and, in particular, condence sets. We present exemplary results for the adaptive Lasso estimator and discuss why the approach often taken in the literature only gives partial answers.

Denis Chetverikov (UCLA, USA)

Nonparametric instrumental variable estimation under monotonicity

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Victor Chernozhukov (MIT, USA)

Gaussian approximations, bootstrap, and Z-estimators when p > > n

Abstract: Gaussian approximations, bootstrap, and Z-estimators when p > > n

Qian Michelle Zhou (Simon Fraser University)

Goodness-of-fit test for model specification

Abstract:In this talk, I will introduce information ratio (IR) statistic to test for model misspecification in various models. The IR test was first proposed in my Ph.D. thesis to test for model misspecification of variance/covariance structure in quasi-likelihood inference for cross-sectional data or longitudinal data. The statistic is constructed via a contrast between two forms of information matrix: the negative sensitivity matrix and variability matrix. Under the null hypothesis that the variance/covariance structure is correctly specified, we show that the proposed test statistic is asymptotically distributed as a normal random variable with mean equal to the dimension of the parameter space. Later, this test was further developed to test for model misspecification on parametric structures in stochastic diffuse models. Afterwards, we extend our method to test for model misspecification in parametric copula functions of semi-parametric copula models. We propose a new test constructed via the contrast between "in-sample" and "out-of-sample" pseudo-likelihoods.

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Dr. Markus Bibinger (HU Berlin)

Statistics of discretely observed semi-martingales under noise

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Jonas Peters (ETH Zürich)

Invariant prediction and causal inference

Abstract:Why are we interested in the causal structure of a data-generating process? In a classical regression problem, for example, we include a variable into the model if it improves the prediction; it seems that no causal knowledge is required. In many situations, however, we are interested in the system's behavior under a change of environment. Here, causal models become important because they are usually considered invariant under those changes. A causal prediction (which uses only direct causes of the target variable as predictors) remains valid even if we intervene on predictor variables or change the whole experimental setting. In this talk, we propose to exploit invariant prediction for causal inference: given data from different experimental settings, we use invariant models to estimate the set of causal predictors. We provide valid confidence intervals and examine sufficient assumptions under which the true set of causal predictors becomes identifiable. The empirical properties are studied for various data sets, including gene perturbation experiments. This talk does not require any prior knowledge about causal concepts.

Prof. Markus Haltmeier (Universität Innsbruck)

Extreme value analysis of frame coefficients and applications

Abstract:Consider the problem of estimating a high-dimensional vector from linear observations that are corrupted by additive Gaussian white noise. Many solution approaches for such problems construct an estimate as the most regular element satisfying a bound on the coefficients of the residuals with respect to some frame. In order that the true parameter is feasible, the coefficients of the noise must satisfy the bound. For that purpose we compute the asymptotic distribution of these coefficients. We show that generically a standard Gumbel law results, as it is known from the case of orthonormal bases. However, for highly redundant frames other limiting laws may occur. We discuss applications of such results for thresholding in redundant wavelet or curvelet frames, and for the Dantzig selector.

Martin Wahl (Universität Mannheim)

Nonparametric estimation in the presence of complex nuisance components

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