Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Consistency of restricted maximum likelihood estimators of principal
  components   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.

30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th