ConvolutionMatrix

If <code>x</code> and <code>s</code> are n- and m-vectors, respectively, returns the n-by-m matrix
of convolution values using Gaussian kernel with bandwidth <code>h</code>. If <code>x</code> and
<code>s</code> are equal, the spectral shift is done to ensure the matrix is numerically
positive definite.

internal

Implements methods for obtaining kernel density estimates
subject to a variety of shape constraints (unimodality, bimodality,
symmetry, tail monotonicity, bounds, and constraints on the number of
inflection points). Enforcing constraints can eliminate unwanted waves or
kinks in the estimate, which improves its subjective appearance and can
also improve statistical performance. The main function scdensity() is
very similar to the density() function in 'stats', allowing
shape-restricted estimates to be obtained with little effort. The
methods implemented in this package are described in Wolters and Braun
(2017) <doi:10.1080/03610918.2017.1288247>, Wolters (2012)
<doi:10.18637/jss.v047.i06>, and Hall and Huang (2002)
<https://www3.stat.sinica.edu.tw/statistica/j12n4/j12n41/j12n41.htm>.
See the scdensity() help for for full citations.

Mark A Wolters

scdensity

Shape-Constrained Kernel Density Estimation

ConvolutionMatrix function

<dl><dt>x</dt>
<dd>A numeric vector.</dd>
<dt>s</dt>
<dd>A numeric vector.</dd>
<dt>h</dt>
<dd>A positive bandwidth.</dd>
<dt>threshold</dt>
<dd>Threshold value passed to SpectralShift.</dd></dl>

Arguments

Computes a matrix of Gaussian kernel convolution values given two vectors. — ConvolutionMatrix

<dl>

<dt>x</dt>
<dd>A numeric vector.</dd>


<dt>s</dt>
<dd>A numeric vector.</dd>


<dt>h</dt>
<dd>A positive bandwidth.</dd>


<dt>threshold</dt>
<dd>Threshold value passed to SpectralShift.</dd>

</dl>

ConvolutionMatrix: Computes a matrix of Gaussian kernel convolution values given two vectors.

Description

Usage

Value

Arguments