projected_differences {covsep}

Compute the projection of the rescaled difference between the sample covariance and its separable approximation onto the separable eigenfunctions

Description

Compute the projection of the rescaled difference between the sample covariance and its separable approximation onto the separable eigenfunctions

Usage

projected_differences(Data, l1 = 1, l2 = 1,
  with.asymptotic.variances = TRUE)

Arguments

Data

a (non-empty) N x d1 x d2 array of data values. The first direction indices the N observations, each consisting of a d1 x d2 discretization of the surface, so that Data[i,,] corresponds to the i-th observed surface.

l1

number of eigenfunctions to be used in the first (row) dimension for the projection

l2

number of eigenfunctions to be used in the second (column) dimension for the projection

with.asymptotic.variances

logical variable; if TRUE, the function outputs the estimate asymptotic variances of the projected differences

Value

A list with

T.N

The projected differences

sigma.left

The row covariances of T.N

sigma.right

The column covariances of T.N

Details

The function computes the projection of the rescaled difference between the sample covariance and its separable approximation onto the separable eigenfunctions u_i x v_j : i = 1, ..., l1; j = 1, ..., l2.

Examples

Data  <-  rmtnorm(30, C1, C2)
ans <- projected_differences(Data, l1=1, l2=2)