Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Optimal Reconstruction of Partially Observed Functional Data   We propose a new reconstruction operator that aims to recover the missing
parts of a function given the observed parts. This new operator belongs to a
new, very large class of functional operators which includes the classical
regression operators as a special case. We show the optimality of our
reconstruction operator and demonstrate that the usually considered regression
operators generally cannot be optimal reconstruction operators. Our estimation
theory allows for autocorrelated functional data and considers the practically
relevant situation in which each of the $n$ functions is observed at $m_i$,
$i=1,\dots,n$, discretization points. We derive rates of consistency for our
nonparametric estimation procedures using a double asymptotic. For data
situations, as in our real data application where $m_i$ is considerably smaller
than $n$, we show that our functional principal components based estimator can
provide better rates of convergence than conventional nonparametric smoothing
methods.

34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg