Dr. Dan Shen
Department of Statistics, University of North Carolina
Title :
PCA Asymptotics and Application in Image Analysis
Date and Time: February 6, 2014 - 4:15pm to 5:15pm
Location: Cupples I, Room 199
Abstract:
The Whittle likelihood is a computationally efficient and matrix-free
Gaussian likelihood approximation that has enjoyed great success in
fitting parametric models to evenly-spaced time series data. There are
multidimensional versions of the Whittle likelihood that can be used to
fit stationary Gaussian models to rectangular spatial lattice data, but
applied in its most naive form, the Whittle likelihood produces
parameter estimates that are not root-n consistent. To alleviate these
issues, data tapers can be employed and have been shown to have the
ability to produce asymptotically efficient parameter estimates in two
and three dimensions. However, for highly correlated data, significant
amounts of tapering are usually required, which leads to noticeable
losses in efficiency in finite samples, especially in three or more
dimensions. We outline a new computationally efficient estimation
framework that employs an augmentation of the spatial lattice data and
MCMC estimation to overcome the deficiencies in data tapering with the
Whittle likelihood. The new framework naturally handles multivariate
data and missing observations as well and thus can be applied to
lattice data with irregular boundaries. We demonstrate the
effectiveness of the new methods in various simulation studies and
apply them to multivariate soil composition data.