/tags/2015-winter/index.xml 2015 Winter - McGill Statistics Seminars

2015 Winter

  • Simultaneous white noise models and shrinkage recovery of functional data

    Fang Yao · Jan 16, 2015

    Date: 2015-01-16

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    We consider the white noise representation of functional data taken as i.i.d. realizations of a Gaussian process. The main idea is to establish an asymptotic equivalence in Le Cam’s sense between an experiment which simultaneously describes these realizations and a collection of white noise models. In this context, we project onto an arbitrary basis and apply a novel variant of Stein-type estimation for optimal recovery of the realized trajectories. A key inequality is derived showing that the corresponding risks, conditioned on the underlying curves, are minimax optimal and can be made arbitrarily close to those that an oracle with knowledge of the process would attain. Empirical performance is illustrated through simulated and real data examples.

  • Functional data analysis and related topics

    Fang Yao · Jan 15, 2015

    Date: 2015-01-15

    Time: 16:00-17:00

    Location: CRM 1360 (U. de Montréal)

    Abstract:

    Functional data analysis (FDA) has received substantial attention, with applications arising from various disciplines, such as engineering, public health, finance etc. In general, the FDA approaches focus on nonparametric underlying models that assume the data are observed from realizations of stochastic processes satisfying some regularity conditions, e.g., smoothness constraints. The estimation and inference procedures usually do not depend on merely a finite number of parameters, which contrasts with parametric models, and exploit techniques, such as smoothing methods and dimension reduction, that allow data to speak for themselves. In this talk, I will give an overview of FDA methods and related topics developed in recent years.

  • Mixtures of coalesced generalized hyperbolic distributions

    Ryan P. Browne · Jan 13, 2015

    Date: 2015-01-13

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    A mixture of coalesced generalized hyperbolic distributions is developed by joining a finite mixture of generalized hyperbolic distributions with a mixture of multiple scaled generalized hyperbolic distributions. The result is a mixture of mixtures with shared model parameters and common mode. We begin by discussing the generalized hyperbolic distribution, which has the t, Gaussian and others as special cases. The generalized hyperbolic distribution can represented as a normal-variance mixture using a generalized inverse Gaussian distribution. This representation makes it a suitable candidate for the expectation-maximization algorithm. Secondly, we discuss the multiple scale generalized hyperbolic distribution which arises via implementation of a multi-dimensional weight function. A parameter estimation scheme is developed using the ever-expanding class of MM algorithms and the Bayesian information criterion is used for model selection. Special consideration is given to the contour shape. We use the coalesced distribution for clustering and compare them to finite mixtures of skew-t distributions using simulated and real data sets. Finally, the role of generalized hyperbolic mixtures within the wider model-based clustering, classification, and density estimation literature is discussed.

  • Space-time data analysis: Out of the Hilbert box

    James O. Ramsay · Jan 9, 2015

    Date: 2015-01-09

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Given the discouraging state of current efforts to curb global warming, we can imagine that we will soon turn our attention to mitigation. On a global scale, distressed populations will turn to national and international organizations for solutions to dramatic problems caused by climate change. These institutions in turn will mandate the collection of data on a scale and resolution that will present extraordinary statistical and computational challenges to those of us viewed as having the appropriate expertise. A review of the current state of our space-time data analysis machinery suggests that we have much to do. Most of current spatial modelling methodology is based on concepts translated from time series analysis, is heavily dependent on various kinds of stationarity assumptions, uses the Gaussian distribution to model data and depends on a priori coordinate systems that do not exist in nature. A way forward from this restrictive framework is proposed by modelling data over textured domains using layered coordinate systems.