Research Seminar

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Autumn Semester 2011

Date / Time

Speaker

Title

Location

21 October 2011
15:15-16:30

Marco Scarsini
LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli

Event Details

Research Seminar in Statistics

Title	Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators
Speaker, Affiliation	Marco Scarsini, LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli
Date, Time	21 October 2011, 15:15-16:30
Location	HG G 19.1
Abstract	We compare estimators of the (essential) supremum and the integral of a function f defined on a measurable space when f may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their levels of stratification of the domain, with the result that more refined stratification is better with respect to different criteria. The emphasis is on criteria related to stochastic orders. For example, rather than compare estimators of the integral of f by their variances (for unbiased estimators), or mean square error, we attempt the stronger comparison of convex order when possible. For the supremum, the criterion is based on the stochastic order of estimators. with Larry Godstein and Yosi Rinott

Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimatorsread_more

HG G 19.1

11 November 2011
15:15-16:30

Florian Frommlet
Universität Wien

Event Details

Research Seminar in Statistics

Title	Modifications of BIC for model selection under sparsity: Theory and applications in genetics
Speaker, Affiliation	Florian Frommlet, Universität Wien
Date, Time	11 November 2011, 15:15-16:30
Location	HG G 19.1
Abstract	In many research areas today the number of features p for which data is collected is much larger than the sample size n based on which inference is made. This is especially true for genetical applications like QTL mapping or genome wide association studies (GWAS). Sparsity is a key notion to be able to perform statistical analysis when p >> n. It means that the number of true signals is small compared with the sample size. This talk will focus on certain modifications of Schwarz's Bayesian information criterion (mBIC and mBIC2) which have been developed to perform model selection under sparsity. These selection criteria are designed in such a way that in case of orthogonal regressors mBIC controls the family wise error rate, while mBIC2 controls the false discovery rate. After introducing the notion of asymptotic Bayes optimality under sparsity (ABOS) we will present recent results concerning some classical multiple testing procedures: While the Bonferroni procedure is ABOS only in case of extreme sparsity, it turns out that the Benjamini Hochberg procedure nicely adapts to the unknown level of sparsity. These results can be translated for mBIC and mBIC2 in the context of model selection. While the theory has been developed so far only for the case of orthogonal designs, simulation studies indicate that good properties of mBIC and mBIC2 also hold in more general situations. We will discuss the case of densely spaced markers in QTL mapping with experimental populations, where specific theory has been developed how to consider the correlation structure of markers. Finally we will present results from a comprehensive simulation study based on real SNP data, which illustrate the relevance of our approach to analyze GWAS data.

Modifications of BIC for model selection under sparsity: Theory and applications in geneticsread_more

HG G 19.1

18 November 2011
15:15-16:30

Davy Paindaveine
Universität Brüssel

Event Details

Research Seminar in Statistics

Title	Semiparametrically Efficient Inference Based On Signed Ranks In Symmetric Independent Component Models
Speaker, Affiliation	Davy Paindaveine, Universität Brüssel
Date, Time	18 November 2011, 15:15-16:30
Location	HG G 19.1
Abstract	We consider semiparametric location-scatter models for which the p-variate observation is obtained as X = ΛZ + μ, where μ is a p-vector, Λ is a full-rank p × p matrix, and the (unobserved) random p-vector Z has marginals that are centered and mutually independent but are otherwise unspecified. As in blind source separation and independent component analysis (ICA), the parameter of interest throughout the paper is Λ. On the basis of n i.i.d. copies of X, we develop, under a symmetry assumption on Z, signed-rank one-sample testing and estimation procedures for Λ. We exploit the uniform local and asymptotic normality (ULAN) of the model to define signed-rank procedures that are semiparametrically efficient under correctly specified densities. Yet, as usual in rank-based inference, the proposed procedures remain valid (correct asymptotic size under the null, for hypothesis testing, and root-n consistency, for point estimation) under a very broad range of densities. We derive the asymptotic properties of the proposed procedures and investigate their finite-sample behavior through simulations.

Semiparametrically Efficient Inference Based On Signed Ranks In Symmetric Independent Component Modelsread_more

HG G 19.1

25 November 2011
15:15-16:30

Yanyuan Ma
Texas A&M University, Department of Statistics

Event Details

Research Seminar in Statistics

Title	A Semiparametric View to Dimension Reduction
Speaker, Affiliation	Yanyuan Ma, Texas A&M University, Department of Statistics
Date, Time	25 November 2011, 15:15-16:30
Location	HG G 19.1
Abstract	We provide a novel and completely different approach to dimension reduction problems from the existing literature. We cast the dimension reduction problem in a semiparametric estimation framework and derive estimating equations. Viewing this problem from the new angle allows us to derive a rich class of estimators, and obtain the classical dimension reduction techniques as special cases in this class. The semiparametric approach also reveals that in the inverse regression context while keeping the estimation structure intact, the common assumption of linearity and/or constant variance on the covariates can be removed at the cost of performing additional nonparametric regression. The semiparametric estimators without these common assumptions are illustrated through simulation studies and a real data example.

A Semiparametric View to Dimension Reductionread_more

HG G 19.1

2 December 2011
15:15-16:30

Genton Marc G.
Texas A&M University, Department of Statistics

Event Details

Research Seminar in Statistics

Title	Functional Boxplots for Visualization of Complex Curve/Image Data: An Application to Precipitation and Climate Model Output
Speaker, Affiliation	Genton Marc G., Texas A&M University, Department of Statistics
Date, Time	2 December 2011, 15:15-16:30
Location	HG G 19.1
Abstract	In many statistical experiments, the observations are functions by nature, such as temporal curves or spatial surfaces/images, where the basic unit of information is the entire observed function rather than a string of numbers. For example the temporal evolution of several cells, the intensity of medical images of the brain from MRI, the spatio-temporal records of precipitation in the U.S., or the output from climate models, are such complex data structures. Our interest lies in the visualization of such data and the detection of outliers. With this goal in mind, we have defined functional boxplots and surface boxplots. Based on the center outwards ordering induced by band depth for functional data or surface data, the descriptive statistics of such boxplots are: the envelope of the 50% central region, the median curve/image and the maximum non-outlying envelope. In addition, outliers can be detected in a functional/surface boxplot by the 1.5 times the 50% central region empirical rule, analogous to the rule for classical boxplots. We illustrate the construction of a functional boxplot on a series of sea surface temperatures related to the El Nino phenomenon and its outlier detection performance is explored by simulations. As applications, the functional boxplot is demonstrated on spatio-temporal U.S. precipitation data for nine climatic regions and on climate general circulation model (GCM) output. Further adjustments of the functional boxplot for outlier detection in spatio-temporal data are discussed as well. The talk is based on joint work with Ying Sun.

Functional Boxplots for Visualization of Complex Curve/Image Data: An Application to Precipitation and Climate Model Outputread_more

HG G 19.1

15 December 2011
16:15-17:30

Johannes Textor
Universität Utrecht

Event Details

Research Seminar in Statistics

Title	Using Causal Diagrams to Dissect Causal from Biasing Effects
Speaker, Affiliation	Johannes Textor, Universität Utrecht
Date, Time	15 December 2011, 16:15-17:30
Location	HG G 19.1
Abstract	A causal diagram (also called Bayesian network, graphical model, or DAG) encodes assumptions about causal relationships between a set of observed and unobserved variabels of interest. Provided that the encoded assumptions are correct, one can use the causal diagram to determine whether and how it is possible to estimate a causal effect of interest from observed (non-experimental) data by means of covariate adjustment. This is a key methodological issue in empirical disciplines like epidemiology, psychology, and the social sciences. Depending on the type of causal effect to be estimated (e.g. total, direct, or mediated effect), there exist different criteria for deciding on the validity of adjustment for a given covariate set. Unfortunately, most of the existing criteria are not complete in the sense that an adjustment may still be valid even if criterion is violated. Moreover, they lead to exponential time algorithms, which may be prohibitive for even moderately sized diagrams. We propose a new criterion that unifies several existing criteria, and is both sound and complete. Moreover, we discuss under which circumstances it is possible to efficiently enumerate all minimal covariate set in a causal diagram that fulfill the criterion. Finally, we shortly describe our implementation of this method in the open source tool DAGitty (www.dagitty.net), and outline its relevance in current epidemiological research.

Using Causal Diagrams to Dissect Causal from Biasing Effectsread_more

HG G 19.1

* 20 January 2012
15:15-16:30

Boaz Nadler
Weizmann Institute of Science, Israel

Event Details

Research Seminar in Statistics

Title	On Roy's largest root test for signal detection in noise, MANOVA and canonical correlation analysis
Speaker, Affiliation	Boaz Nadler, Weizmann Institute of Science, Israel
Date, Time	20 January 2012, 15:15-16:30
Location	HG G 19.1
Abstract	Roy's largest root is one of the four most common tests in multivariate analysis of variance (MANOVA), with applications in many other problems, including signal detection in noise, and canonical correlation analysis. The other three popular tests, namely Wilks Lambda, Hotelling-Lawley trace and Pillai-Bartlett trace, have been thoroughly studied, and accurate F-type approximations to their distributions have been derived. In contrast, accurate and tractable approximations to the distribution of Roy's largest root test have so far resisted such analysis and remained an open problem for several decades. In this talk, I'll derive a simple yet accurate approximation for the distribution of Roy's largest root test, in the extreme case of a rank-one alternative, also known as concentrated non-centrality, where the difference between groups is concentrated in a single direction, or similarly only a single signal is present. Our results allow power calculations for Roy's test, and provide a lower bound on the minimal number of samples required to detect a given group difference, or a given signal strength. Joint work with Iain Johnstone (Stanford).

On Roy's largest root test for signal detection in noise, MANOVA and canonical correlation analysisread_more

HG G 19.1

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Organizers: Peter Bühlmann, Leonhard Held, Hansruedi Künsch, Sara van de Geer, Michael Wolf

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