Paper: Nov 15,2019
stat.ME
ID:1911.06583
GET: Global envelopes in R
This work describes the R package GET that implements global envelopes for a
general set of $d$-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 $\alpha$. The term 'global' means that this probability is controlled
simultaneously for all the $d$ elements of the vectors. The global envelopes
can be employed for central regions of functional or multivariate data, for
graphical Monte Carlo and permutation tests where the test statistic is
multivariate or functional, and for global confidence and prediction bands.
Intrinsic graphical interpretation property is introduced for global envelopes.
The global envelopes included in the GET package have this property, which
particularly helps to interpret test results, by providing a graphical
interpretation that shows the reasons of rejection of the tested hypothesis.
Examples of different uses of global envelopes and their implementation in the
GET package are presented, including global envelopes for single and several
one- or two-dimensional functions, Monte Carlo goodness-of-fit tests for simple
and composite hypotheses, comparison of distributions, functional analysis of
variance, functional linear model, and confidence bands in polynomial
regression.
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Paper Author: Mari Myllymäki,Tomáš Mrkvička
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