Date: 2012-03-02

Time: 15:30-16:30

Location: BURN 1205

Abstract:

In functional data analysis, as in its multivariate counterpart, estimates of the bivariate covariance kernel σ(s,t ) and its inverse are useful for many things, and we need the inverse of a covariance matrix or kernel especially often. However, the dimensionality of functional observations often exceeds the sample size available to estimate σ(s,t, and then the analogue S of the multivariate sample estimate is singular and non-invertible. Even when this is not the case, the high dimensionality S often implies unacceptable sample variability and loss of degrees of freedom for model fitting. The common practice of employing low-dimensional principal component approximations to σ(s,t) to achieve invertibility also raises serious issues.

This talk describes a functional estimate of σ(s,t) and its inverse defined by an expansion in terms of finite element basis functions. This strategy permits the user to control the resolution of the estimate, its smoothness, and the time lag over which covariance may be nonzero. It turns out that the matrix resulting from evaluating σ(s,t) at a discrete set of time points is almost never singular, and therefore enables the estimation of S and S-1 as a seamless single problem. These estimates have many applications to classical statistical problems, such as discrete but unequally spaced time and spatial series, as well as to functional and longitudinal data analysis.

Speaker

Jim Ramsay is a leading researcher in the area of Functional Data Analysis. He is a Professor Emeritus at the Department of Psychology, McGill University.