DR.basis

Calculates the periodic Demmler-Reinsch basisfor a given smoothness and a given vector of grid points. For details see (Schwarz, Krivobokova; 2016).

A nonparametric method to estimate Toeplitz covariance matrices from a sample of n independently and identically distributed p-dimensional vectors with mean zero. The data is preprocessed with the discrete cosine matrix and a variance stabilization transformation to obtain an approximate Gaussian regression setting for the log-spectral density function. Estimates of the spectral density function and the inverse of the covariance matrix are provided as well. Functions for simulating data and a protein data example are included. For details see (Klockmann, Krivobokova; 2023), <arXiv:2303.10018>.

Karolina Klockmann

vstdct

Nonparametric Estimation of Toeplitz Covariance Matrices

Tatyana Krivobokova

DR.basis function

<dl><dt>x</dt>
<dd><code>m</code>-dim. vector with grid values in [0,1]</dd>
<dt>n</dt>
<dd>dimension of the basis</dd>
<dt>q</dt>
<dd>penalization order, <code>q=1,2,3,4</code> are available</dd></dl>

Arguments

Periodic Demmler-Reinsch Basis — DR.basis

<dl>

<dt>x</dt>
<dd><code>m</code>-dim. vector with grid values in [0,1]</dd>


<dt>n</dt>
<dd>dimension of the basis</dd>


<dt>q</dt>
<dd>penalization order, <code>q=1,2,3,4</code> are available</dd>

</dl>

DR.basis: Periodic Demmler-Reinsch Basis

Description

Usage

Value

Arguments

Examples