# The LiU Seminar Series in Statistics and Mathematical Statistics

### Tuesday, September 2, 3.15 pm, 2014. Seminar in Mathematical Statistics.

**Tests For Covariance Matrices in High Dimension with Less Sample Size**

Muni S. Srivastava, Department of Statistical Sciences, University of Toronto, Canada.

Muni S. Srivastava

*Abstract*: In this article, we propose tests for covariance matrices of high dimension with fewer observations than the dimension for a general class of distributions with positive definite covariance matrices. In one-sample case, tests are proposed for sphericity and for testing the hypothesis that the covariance matrix bSi is an identity matrix, by providing an unbiased estimator of tr[bSi2] under the general model which requires no more computing time than the one available in the literature for normal model. In the two-sample case, tests for the equality of two covariance matrices are given. The asymptotic distributions of proposed tests in one-sample case are derived under the assumption that the sample size N = O(p^{delta}), 1/2 < delta <1, where p is the dimension of the random vector.

Keywords & Phrases: Asymptotic distributions, covariance matrix, high dimension, non-normal model, sample size smaller than dimension, test statistics.

Location: Hopningspunkten.

### Tuesday, September 9, 3.15 pm, 2014. Seminar in Statistics.

**Developing Neuroimaging Methods to Disentangle Mild Traumatic Brain Injury**

Erik Eierud, Baylor College of Medicine, USA.

Erik Eierud

*Abstract*: In the 4th century BC, mild traumatic brain injury (mTBI) was defined, but until recently, sparse work to track or alleviate effects from mTBI has materialized. Perhaps reasons are that many other important injuries are discovered and treatable using modern technology, while mTBI injuries are obscure and often untreatable despite impressive improvements in neuroimaging and other mTBI related techniques. Since 1990 there has been an upsurge in mTBI-neuroimaging literature, which is the focus of this presentation. Extra attention will be given to diffusion tensor imaging (DTI) and functional MRI (fMRI). For fMRI we have explored support vector machines with goal to track the mTBI progression over time after injury. In addition, we have explored a naive model system to validate our mTBI-fMRI methods. Finally we will present results from 10 mTBI subjects, which we have measured longitudinally, within a year after their concussion.

Location: Alan Turing

### Tuesday, September 23, 3.15 pm, 2014. Seminar in Mathematical Statistics.

**On Random Geometric Subdivisions**

Stanislav Volkov, Mathematical Statistics, Lund University.

Stanislav Volkov

*Abstract*: I will present several models of random geometric subdivisions, similar to that of Persi Diaconis and Laurent Miclo (Combinatorics, Probability and Computing, 2011), where a triangle is split into 6 smaller triangles by its medians, and one of these parts is randomly selected as a new triangle, and the process continues ad infinitum. I will show that in a similar model the limiting shape of an indefinite subdivision of a quadrilateral is a parallelogram. I will also show that the geometric subdivisions of a triangle by angle bisectors converge (but only weakly) to a non-atomic distribution, and that the geometric subdivisions of a triangle by choosing a uniform random points on its sides converges to a flat triangle, similarly to the result of the paper mentioned above.

Location: Hopningspunkten.

### Tuesday, October 7, 3.15 pm, 2014. Seminar in Mathematical Statistics.

**Confidence distributions and nuisance parameters**

Rolf Larsson, Mathematical Statistics, Stockholm University.

Rolf Larsson

*Abstract*: We study hypothesis testing using confidence distributions for two parameters, where one of them is of interest and the other one is a nuisance parameter. Under asymptotic normality of parameter estimates, we introduce a framework where the ideas of integrating out or maximizing w.r.t the nuisance parameter (profiling) appear as extreme cases. In particular, three examples are considered: testing that the higher order parameter in an autoregressive process of order two is zero, testing that the moving average parameter is zero in the simplest autoregressive moving average model, ARMA(1,1), and testing equality of two binomial proportions. Overall, integrating is to be preferred over profiling, although problems can occur in the ARMA case due to identification issues. Moreover, in the binomial example, we illustrate how we may find a useful compromise between the two methods in terms of robustness of size when varying the nuisance parameter.

Location: Hopningspunkten.

### Tuesday, October 21, 3.15 pm, 2014. Seminar in Statistics.

**Empirically Informed Statistical Simulation Models for the Social Sciences - an Application to Residential segregation in Stockholm**

Johan Koskinen, Social Statistics DA, University of Manchester.

Johan Koskinen

*Abstract*: Residential segregation along ethnic and socio-economic lines has been identified as one of the most pressing problems being faced by Swedish society nowadays. So far, the underlying processes have mostly been studied in isolation. We propose a dynamic, discrete choice model that draws on recent advances in modelling of complex dynamic networks. The empirical application concerns the sequences of annual residential moves in the Stockholm municipal area between 1991-2003. We have data on all individuals in the Stockholm municipal area including their country of birth, levels and sources of income, employment characteristics as well as their place of residence for each year. At each point in time, data may be represented by a row-regular binary affiliation matrix where Yij=1 if an individual i=1,...,n lives in the Small Area Market Statistics (SAMS) area j=1,...,m. Here m = 128 and n is roughly 500k. We first demonstrate the rich interdependencies inherent in the data by exploring exponential random graph models for the 'moving graph' aggregated to SAMS. We then proceed to specify a stochastic actor oriented model (SAOM), a discrete Markov chain in continuous time inspired by Snijders (2001), for the individual movements where the elements Yij=1 and Yih=0 are swapped for some h and j. We assume a SAOM where the sequences of moves are modelled through conditional logistic regression models (CLGT) with endogenously changing option sets for individuals. We focus on the subset of individuals that have already decided to move and thus we do not explicit model the decision to move. Competition for scarce resources thus only enter indirectly through the sequential conditioning over time. The SAOM introduces parameters for the following basic effects: the popularity of neighbourhoods; preferences for moving into an area with matching ethnic/socio-economic composition; preferences for areas that are geographically close to the current place of residence; preferences for moving into area where an individual has kin. We furthermore discuss the construction of relevant constraints on the housing market. Estimation is carried out using a Bayesian data-augmentation, Markov chain Monte Carlo scheme that treats the order of the moves in-between yearly observations as missing data. The underlying Markov chain readily lends itself to simulation of the inferred social processes, thus providing a micro-simulation tool for exploring properties of the model in great detail. We suggest that the possibility of pursuing such empirically informed simulation models is underused and under-developed - the actor-oriented simulation model affords unpacking the complex dynamics of a social system in an empirically testable framework.

Location: Alan Turing

### Tuesday, November 4, 3.15 pm, 2014. Seminar in Mathematical Statistics.

**On the Existence of Fake Brownian Motions**

Patrik Albin, Mathematical Statistics, Chalmers University.

Patrik Albin

*Abstract*: We construct a continuous martingale {M(t); t≥0} with the same univariate marginal distributions N(0,t) as Brownian motion, but that is not Brownian motion. We learned about this problem some years ago from a seminar given by Fima C Klebaner at Chalmers and solved it some time thereafter.

Location: Hopningspunkten.

### Tuesday, November 18, 3.15 pm, 2014. Seminar in Statistics.

**Higher criticism, detection boundary, high dimensionality, supervised classification, separation strength.**

Annika Tillander, Dept. of Medical Epidemiology and Biostatistics.

Annika Tillander

*Abstract*: The analysis of high-throughput data commonly used in modern applications poses many statistical challenges, one of which is the selection of a small subset of features that are likely to be informative for a specific project. This issue is crucial for success of supervised classification in very high-dimensional setting with sparsity patterns. Here we derive an asymptotic framework that represents sparse and weak blocks model and suggest a technique for block-wise feature selection by thresholding. Our procedure extends the standard Higher Criticism (HC) thresholding to the case where dependence structure underlying the data can be taken into account and is shown to be optimally adaptive, i. e. performs well without knowledge of the sparsity and weakness parameters. We empirically investigate the detection boundary of our HC procedure and performance properties of some estimators of sparsity parameter. The relevance and benefits of our approach in high-dimensional classification is demonstrated using both simulation and real data.

Location: Alan Turing

### Tuesday, December 2, 3.15 pm, 2014. Seminar in Statistics.

**Covariate selection based on Directed Acyclic Graphs**

Arvid Sjölander, Dept. of Medical Epidemiology and Biostatistics.

Arvid Sjölander

*Abstract*: The aim of (epidemiological) research is often to estimate the causal effect of a particular exposure on a particular outcome. In observational (i.e. non-randomized) studies, an observed exposure-outcome association can only be given a causal interpretation if one adjusts for all covariates that "confound" the association. To select which covariates to adjust for is a non-trivial task, and traditional selection strategies are associated with problems that are often overlooked. In this seminar we present a selection strategy based Directed Acyclic Graphs, which does not suffer from the problems associated with the traditional strategies. We present the underlying theory, and some concrete examples.

Location: Alan Turing

## Past Seminars

Spring 2014 | Fall 2013 | Spring 2013 | Fall 2012 | Spring 2012 | Fall 2011
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Last updated: 2014-11-12