# The LiU Seminar Series in Statistics and Mathematical Statistics

### Tuesday, January 19, 1.15 pm, 2016. Seminar in Mathematical Statistics.

**On Skewed Multivariate Distributions**

Tönu Kollo, Institute of Mathematics and Statistics, University of Tartu.

Tönu Kollo

*Abstract*: Skew-symmetric elliptical distributions will be of interest and estimation of their parameters discussed. Explicit expressions of the estimators by the method of moments are presented for some distributions with help of multivariate skewness and kurtosis measures. Construction of copulas from skew-elliptical distributions is considered and some properties of these copulas is discussed.

Location: Hopningspunkten.

### Tuesday, January 26, 3.15 pm, 2016. Seminar in Mathematical Statistics.

**Large deviations for longest runs**

Xiangfeng Yang, Mathematical Statistics, Linköping University

Xiangfeng Yang

*Abstract*: In the first n tosses of a coin, the longest head/success run L(n) is the longest stretch of consecutive heads/successes. The same definition can be also given in the first n steps of a two-state Markov chain. The longest run is the basic object in a consecutive-k-out-of-n system, and it finds other applications such as in statistics. In this talk we will firstly review some well known properties of L(n), and then present several new results on large deviations of L(n). An application in statistical inference will be mentioned as well, together with several possible extensions such as comparing two DNA sequences.

Location: Hopningspunkten.

### Tuesday, February 9, 3.15 pm, 2016. Seminar in Statistics.

**Why fMRI inferences for spatial extent have inflated false positive rates**

Anders Eklund, IDA and IMT, Linköping University

Anders Eklund

*Abstract*: The most widely used task functional magnetic resonance imaging (fMRI) analyses use parametric statistical methods that depend on a variety of assumptions. While individual aspects of these fMRI models have been evaluated, they have not been evaluated in a comprehensive manner with empirical data. In this work, a total of 2 million random task fMRI group analyses have been performed using resting state fMRI data, to compute empirical familywise error rates for the fMRI software packages SPM, FSL and AFNI, as well as a standard non-parametric permutation method. While there is some variation, for a nominal familywise error rate of 5% the parametric statistical methods are shown to be conservative for voxel-wise inference and invalid for cluster-wise inference; in particular, cluster size inference with a cluster defining threshold of p = 0.01 generates familywise error rates up to 60%. We conduct a number of follow up analyses and investigations that suggest the cause of the invalid cluster inferences is spatial auto correlation functions that do not follow the assumed Gaussian shape. By comparison, the non-parametric permutation test, which is based on a small number of assumptions, is found to produce valid results for voxel as well as cluster wise inference. Using real task data, we compare the results between one parametric method and the permutation test, and find stark differences in the conclusions drawn between the two using cluster inference. These findings speak to the need of validating the statistical methods being used in the neuroimaging field.

Location: Alan Turing.

### Tuesday, February 23, 3.15 pm, 2016. Seminar in Mathematical Statistics.

**Quantifying the uncertainty of contour maps**

David Bolin, Mathematical Statistics, Chalmers University.

David Bolin

*Abstract*: Contour maps are widely used to display estimates of spatial fields. Instead of showing the estimated field, a contour map only shows a fixed number of contour lines for different levels. However, despite the ubiquitous use of these maps, the uncertainty associated with them has been given a surprisingly small amount of attention. We derive measures of the statistical uncertainty, or quality, of contour maps, and use these to decide an appropriate number of contour lines,that relates to the uncertainty in the estimated spatial field. For practical use in geostatistics and medical imaging, computational methods are constructed, that can be applied to Gaussian Markov random fields, and in particular be used in combination with integrated nested Laplace approximations for latent Gaussian models. The methods are demonstrated on simulated data and an application to temperature estimation is presented.

Location: Hopningspunkten.

### Tuesday, March 8, 3.15 pm, 2016. Seminar in Statistics.

**Are random sample surveys dead?**

Dan Hedlin, Department of Statistics, Stockholm University.

Dan Hedlin

*Abstract*: There is an ongoing debate on self-recruited web panel surveys versus random sample surveys. For example, the Swedish public service news, Ekot, have decided not to report on opinion polls based on self-recruited web panel surveys. They also require a response rate of at least 50%. Are these requirements sensible? Or are they just a sign of conservatism? I will discuss the issues of non-random sampling and nonresponse in surveys and point out some conditions for surveys with nonresponse or non-random samples to be reliable.

Location: Alan Turing.

### Tuesday, March 22, 3.15 pm, 2016. Seminar in Mathematical Statistics.

**Generalised eigenvalues of random matrices and rank of random tensors**

Göran Bergqvist

Göran Bergqvist

*Abstract*: A rank-1 order-d tensor or multi-array is the tensor product of d vectors, and the rank of a tensor T is the minimum number of rank-1 tensors needed in a sum that equals T. Assuming elements of some continuous probability distribution, a random matrix or order-2 tensor has full rank with probability 1. For higher-order real random tensors several ranks can occur with positive probability. We show how knowledge about the distribution of real generalised eigenvalues of random matrices can be used to find rank probabilities for order-3 random tensors of size n x n x 2, and find exact values of rank probabilities for such tensors with independent standard Gaussian entries. These are the only known exact results for tensor rank probabilities. This is partly joint work with Peter Forrester.

Location: Hopningspunkten.

### Tuesday, April 19, 3.15 pm, 2016. Seminar in Mathematical Statistics.

**Stochastic differential equations on non-smooth time-dependent domains**

Thomas Önskog, Mathematical Statistics, KTH

Thomas Önskog

*Abstract*: The Skorohod problem is an important tool for constructing solutions to stochastic differential equations with reflection. In this talk, I give an introduction to the Skorohod problem and show how it can be used to prove existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection on non-smooth time-dependent domains whose boundary is Hölder continuous in time. Crucial to the proof is the construction of certain test functions that can also be used to prove existence and uniqueness of viscosity solutions to fully nonlinear second-order parabolic partial differential equations with oblique derivative boundary conditions. The presented results generalize earlier results by Dupuis and Ishii to the setting of time-dependent domains. The talk is based on joint work with Niklas Lundström at Umeå University.

Location: Hopningspunkten.

### Tuesday, May 3, 3.15 pm, 2016. Seminar in Statistics.

**A Lagrange Multiplier-type Test for Iidiosyncratic Unit Roots in the Exact Factor Model**

Xingwu Zhou, Department of Pharmaceutical Biosciences and Department of Statistics, Uppsala University.

Xingwu Zhou

*Abstract*: In this paper, an exact factor model is considered, and a Lagrange multiplier-type test is derived for a homogeneous unit root in the idiosyncratic component. It is shown that under sequential asymptotics, its null limiting distribution is standard normal, regardless of whether the factors are integrated, cointegrated or stationary. In a simulation study, the asymptotic size and local power of the Lagrange multiplier-type test and some popular non-likelihood based tests are compared. The simulation results show that the Lagrange multiplier-type test has the highest local power as both the time dimension and the cross-sectional dimension tend to infinity, with the actual size tending to the nominal size. Because likelihood-based tests belong to the locally most powerful tests, the simulation results obtained are as expected.

Location: Alan Turing.

### Tuesday, May 17, 3.15 pm, 2016. Seminar in Mathematical Statistics.

**Exact and Asymptotic Tests on a Factor Model in Low and Large Dimensions with Applications**

Taras Bodnar, Mathematical Statistics, Stockholm University

Taras Bodnar

*Abstract*: We suggest three tests on the validity of a factor model which can be applied for both small dimensional and large dimensional data. Both the exact and asymptotic distributions of the resulting test statistics are derived under classical and high-dimensional asymptotic regimes. It is shown that the critical values of the proposed tests can be calibrated empirically by generating a sample from the inverse Wishart distribution with identity parameter matrix. The powers of the suggested tests are investigated by means of simulations. The results of the simulation study are consistent with the theoretical findings and provide general recommendations about the application of each of the three tests. Finally, the theoretical results are applied to two real data sets, which consist of returns on stocks from the DAX index and on stocks from the S&P 500 index. Our empirical results do not support the hypothesis that all linear dependencies between the returns can be entirely captured by the factors considered in the paper.

Location: Hopningspunkten.

### Tuesday, May 24, 3.15 pm, 2016. Seminar in Mathematical Statistics.

**Testing mean under compound symmetry covariance setup**

Daniel Klein, P.J. Safarik University, Slovakia

Daniel Klein

*Abstract*: Geisser 1963 discussed the problem of testing the mean in the normal model under compound symmetry covariance structure. Szatrowski 1982 discussed estimation and testing block compound symmetry problem. Very recently we arrived to the solution of this problem as a natural extension of the Hotelling's T2 test statistic, which seemed to be very easy; the solution was obtained via orthogonal transformation which diagonalize (or block-diagonalize) the variance matrix of the transformed vector. Natural question arrised afterwards: Is the solution independent to this transformation? We will discuss this question.

Location: Hopningspunkten.

### Tuesday, May 31, 3.15 pm, 2016. Seminar in Statistics.

**Testing independence via spectral moments**

Jolanta Pielaszkiewicz, Mathematical Statistics, Linköping University

Jolanta Pielaszkiewicz

*Abstract*: Assume that a matrix X is matrix normally distributed and that the Kolmogorov condition holds. We propose a test for identity of the covariance matrix using a goodness-of-fit approach. Calculations are based on a recursive formula derived by Pielaszkiewicz et al. The test performs well regarding the power compared to presented alternatives.

Location: Alan Turing.

## Past Seminars

Fall 2015 | Spring 2015 | Fall 2014 | Spring 2014 | Fall 2013 | Spring 2013 | Fall 2012 | Spring 2012 | Fall 2011
Page responsible: Mattias Villani

Last updated: 2016-05-31