residual

Subtract the theoretical function \(S_{H_0}\) or the mean of the functions
in the curve set. If the <code>curve_set</code> object contains already residuals
\(T_i(r) - T_0(r)\), <code>use_theo</code> ignored and the same object returned.

Implementation of global envelopes for a set of general d-dimensional vectors T
in various applications. A 100(1-alpha)% global envelope is a band bounded by two
vectors such that the probability that T falls outside this envelope in any of the d
points is equal to alpha. Global means that the probability is controlled simultaneously
for all the d elements of the vectors. The global envelopes can be used for graphical
Monte Carlo and permutation tests where the test statistic is a multivariate vector or
function (e.g. goodness-of-fit testing for point patterns and random sets, functional
analysis of variance, functional general linear model, n-sample test of correspondence
of distribution functions), for central regions of functional or multivariate data (e.g.
outlier detection, functional boxplot) and for global confidence and prediction bands
(e.g. confidence band in polynomial regression, Bayesian posterior prediction). See
Myllymäki and Mrkvička (2024) <doi:10.18637/jss.v111.i03>,
Myllymäki et al. (2017) <doi:10.1111/rssb.12172>,
Mrkvička and Myllymäki (2023) <doi:10.1007/s11222-023-10275-7>,
Mrkvička et al. (2016) <doi:10.1016/j.spasta.2016.04.005>,
Mrkvička et al. (2017) <doi:10.1007/s11222-016-9683-9>,
Mrkvička et al. (2020) <doi:10.14736/kyb-2020-3-0432>,
Mrkvička et al. (2021) <doi:10.1007/s11009-019-09756-y>,
Myllymäki et al. (2021) <doi:10.1016/j.spasta.2020.100436>,
Mrkvička et al. (2022) <doi:10.1002/sim.9236>,
Dai et al. (2022) <doi:10.5772/intechopen.100124>,
Dvořák and Mrkvička (2022) <doi:10.1007/s00180-021-01134-y>,
Mrkvička et al. (2023) <doi:10.48550/arXiv.2309.04746>, and
Konstantinou et al. (2024) <doi: 10.1007/s00180-024-01569-z>.

Mari Myllym<c3><a4>ki

Global Envelopes

Mari Myllymäki

Tomáš Mrkvička

Mikko Kuronen

Jiří Dvořák

Pavel Grabarnik

Ute Hahn

Michael Rost

Henri Seijo

residual function

<dl><dt>curve_set</dt>
<dd>A <code>curve_set</code> object, or
an <code>envelope</code> object of spatstat. If an envelope object is given,
it must contain the summary functions from the simulated patterns which can be
achieved by setting savefuns = TRUE when calling the <code>envelope</code> function.</dd>
<dt>use_theo</dt>
<dd>Whether to use the theoretical summary function or the
mean of the functions in the curve_set.</dd></dl>

Arguments

Residual form of the functions — residual

<dl>

<dt>curve_set</dt>
<dd>A <code>curve_set</code> object, or
an <code>envelope</code> object of spatstat. If an envelope object is given,
it must contain the summary functions from the simulated patterns which can be
achieved by setting savefuns = TRUE when calling the <code>envelope</code> function.</dd>


<dt>use_theo</dt>
<dd>Whether to use the theoretical summary function or the
mean of the functions in the curve_set.</dd>

</dl>

residual: Residual form of the functions

Description

Usage

Value

Arguments

Details