Consistency of restricted maximum likelihood estimators of principal components

Details Consistency of restricted maximum likelihood estimators of principal components Consistency of restricted maximum likelihood estimators of principal components

2008-05-05

arxiv.org/abs/0805.0465v1

Mathematics

Statistics Theory

Scientific paper

In this paper we consider two closely related problems : estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and eigenvectors of the covariance matrix for high-dimensional Gaussian vectors. In Peng and Paul (2007), a restricted maximum likelihood (REML) approach has been developed to deal with the first problem. In this paper, we establish consistency and derive rate of convergence of the REML estimator for the functional data case, under appropriate smoothness conditions. Moreover, we prove that when the number of measurements per sample curve is bounded, under squared-error loss, the rate of convergence of the REML estimators of eigenfunctions is near-optimal. In the case of Gaussian vectors, asymptotic consistency and an efficient score representation of the estimators are obtained under the assumption that the effective dimension grows at a rate slower than the sample size. These results are derived through an explicit utilization of the intrinsic geometry of the parameter space, which is non-Euclidean. Moreover, the results derived in this paper suggest an asymptotic equivalence between the inference on functional data with dense measurements and that of the high dimensional Gaussian vectors.

Affiliated with

Also associated with

No associations

Rating

Consistency of restricted maximum likelihood estimators of principal components does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Consistency of restricted maximum likelihood estimators of principal components, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Consistency of restricted maximum likelihood estimators of principal components will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-208533