“An L2 Test Theory for Nonstationary Time Series”
Dr. Wei Biao Wu, University of Chicago

Date: Tuesday, December 02, 2014
Time: 4:00 PM – 5:00 PM
Location: 269 Everitt
Sponsor: Department of Statistics, Xiaohui Chen

Abstract:
I will discuss testing whether the mean trend of a nonstationary time series is of certain parametric forms. A central limit theorem for the integrated squared error is derived, and with that a hypothesis-testing procedure is proposed. The method is illustrated in a simulation study, and is applied to assess the trend pattern in the central England temperature series. The work is joint with Ting Zhang.

“An L2 Test Theory for Nonstationary Time Series”
Dr. Wei Biao Wu, University of Chicago

Date: Tuesday, December 02, 2014
Time: 4:00 PM – 5:00 PM
Location: 269 Everitt
Sponsor: Department of Statistics, Xiaohui Chen

Abstract:
I will discuss testing whether the mean trend of a nonstationary time series is of certain parametric forms. A central limit theorem for the integrated squared error is derived, and with that a hypothesis-testing procedure is proposed. The method is illustrated in a simulation study, and is applied to assess the trend pattern in the central England temperature series. The work is joint with Ting Zhang.

“L2 Asymptotics for High-Dimensional Data”
Dr. Mengyu Xu, University of Chicago

Date: Thursday, November 20, 2014
Time: 4:00 PM – 5:00 PM
Location: 269 Everitt
Sponsor: Department of Statistics, Xiaohui Chen

Abstract:

We develop an asymptotic theory for L2 norms of sample mean vectors of high-dimensional data. An invariance principle for the L2 norms is derived under conditions that involve a delicate interplay between the dimension p, the sample size n and the moment condition. Under proper normalization, central and non-central limit theorems are obtained. To facilitate the related statistical inference, we propose a plug-in calibration method and a sub-sampling procedure to approximate the distributions of the L2 norms. Our results are applied to multiple tests and inference of covariance matrix structures.

Statistics Seminar

Speaker Dr. Ming Yuan, University of Wisconsin – Madison
Title           “Rate-Optimal Detection of Very Short Signal Segments”
Date            Thursday, October 23, 2014
Time            4:00 PM – 5:00 PM
Location        269 Everitt

Abstract:
Motivated by a range of applications in engineering and genomics, we consider in this paper detection of very short signal segments in three settings: signals with known shape, arbitrary signals, and smooth signals. Optimal rates of detection are established for the three cases and rate-optimal detectors are constructed. The detectors are easily implementable and are based on scanning with linear and quadratic statistics. Our analysis reveals both similarities and differences in the strategy and fundamental difficulty of detection among these three settings.

Statistics Seminar – Dr. Peter Hoff, University of Washington: “Multilinear Models for Relational Tensor Data”

Date            Thursday, October 16, 2014
Time            4:00 PM – 5:00 PM
Location        269 Everitt

Abstract: A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations: How A relates to B may possibly depend on how C relates to B or even how C relates to D. We investigate the possibility of estimating such dependencies from weekly international relations data among countries from 2004-2013. Such data can be represented as a multiway array, or tensor. We develop a multilinear regression model for analysis of such tensor-valued data, discuss some of its properties, and compare it to some more familiar linear regression models.

Statistics Seminar – Dr. Tobias Kley, Ruhr-Universitaet Bochum
“Quantile-Based Spectral Analysis of Time Series”

Date            Friday, October 03, 2014
Time            3:30 pm – 5:00 pm
Location        7 David Kinley Hall

Abstract:
In this talk an alternative approach to the spectral analysis of time series is presented. First, a “new” spectrum is defined for stationary processes {Y_t}_{t in Z}. We call the Fourier transform of the differences between copulas of the pairs (Y_t,Y_t−k) and the independence copula the copula spectral density kernel. This object allows to separate marginal and serial aspects of a time series. The cop- ula intrinsically provides more information about the conditional distribution than the covariance. Thus, the copula spectral density kernel is more informative than the spectral density obtained from the autocovariances. In particular, a complete description of the distributions of all pairs (Y_t,Y_{t−k}) is possible. Two rank-based estimators of the copula spectral density kernel are provided. We establish their asymptotic properties. The results are applicable without restrictive distributional assumptions such as the existence of finite moments and only weak mixing assumptions are necessary. To allow non-stationarity in the analysis, localized versions of the copula spectrum and of the estimators are introduced. We define the concept of local strict stationarity and show consis- tency of a localized estimator under this condition. The R package quantspec will be introduced. A demonstration on how it can be used in the analysis of an empirical example will be given. This is joint work with H. Dette, M. Hallin, S. Skowronek, and S. Volgushev. Dette, H., Hallin, M., Kley, T. and Volgushev, S. (2014+). Of copulas, quantiles, ranks and spectra: An L1-approach to spectral analysis. To appear in Bernoulli. Kley, T., Volgushev, S., Dette, H. and Hallin, M. (2014). Quantile spectral pro- cesses: Asymptotic analysis and inference (arxiv.org/abs/1401.8104). Skowronek, S, Volgushev, S., Kley, T., Dette, H. and Hallin, M. (2014). Quantile spectral analysis for locally stationary time series (arxiv.org/abs/1404.4605). Kley,T. (2014). Quantile-based spectral analysis in an object-oriented frame- work and a reference implementation in R: The quantspec Package (arxiv.org/abs/1408.6755).