A Functional Estimate of Covariation

This article uses finite element methodology to construct a representation of a functional Choleski factor λ( w , s ) to define σ( s , t ) = ∫λ( w , s )λ( w , t ) dw . An estimate of Σ-1 is especially important for applications and, where the eigenstructure of the covariance permits, this is readily available since the resulting Σ is almost always positive definite.

A simulation study compares the performance of estimates of Σ and Σ-1 to those from the classic covariance matrix estimate and an estimate using glasso package in R. The method’s capability of constraining estimates of Σ-1 to be strongly band-structured resulted in superior estimates. The real data application is to the smoothing of the Fels female growth data where σ( s , t ) estimates the residual covariance structure in the presence of sampling points varying from one case to another.