GET: Global envelopes in R

Abstract: 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.