56 research outputs found
GET: Global envelopes in R
This work describes the R package GET that implements global envelopes for a
general set of -dimensional vectors in various applications. A
% global envelope is a band bounded by two vectors such that the
probability that falls outside this envelope in any of the points is
equal to . Global means that the probability is controlled
simultaneously for all the 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,
and the global envelopes included in the GET package that have the property are
described. 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, graphical functional analysis of variance (ANOVA), and general
linear model (GLM), and confidence bands in polynomial regression
False discovery rate envelope for functional test statistics
False discovery rate (FDR) is a common way to control the number of false
discoveries in multiple testing. In this paper, the focus is on functional test
statistics which are discretized into highly correlated hypotheses and thus
resampling based methods are investigated. The aim is to find a graphical
envelope that detects the outcomes of all individual hypotheses by a simple
rule: the hypothesis is rejected if and only if the empirical test statistic is
outside of the envelope. Such an envelope offers a straightforward
interpretation of the test results similarly as in global envelope testing
recently developed for controlling the family-wise error rate. Two different
algorithms are developed to fulfill this aim. The proposed algorithms are
adaptive single threshold procedures which include the estimation of the true
null hypotheses. The new methods are illustrated by two real data examples
Hierarchical second-order analysis of replicated spatial point patterns with non-spatial covariates
In this paper we propose a method for incorporating the effect of non-spatial covariates into the spatial second-order analysis of replicated point patterns. The variance stabilizing transformation of Ripley’s K function is used to summarize the spatial arrangement of points, and the relationship between this summary function and covariates is modelled by hierarchical Gaussian process regression. In particular, we investigate how disease status and some other covariates affect the level and scale of clustering of epidermal nerve fibres. The data are point patterns with replicates extracted from skin blister samples taken from 47 subjects.Peer reviewe
Point process models for sweat gland activation observed with noise
The aim of the paper is to construct spatial models for the activation of
sweat glands for healthy subjects and subjects suffering from peripheral
neuropathy by using videos of sweating recorded from the subjects. The sweat
patterns are regarded as realizations of spatial point processes and two point
process models for the sweat gland activation and two methods for inference are
proposed. Several image analysis steps are needed to extract the point patterns
from the videos and some incorrectly identified sweat gland locations may be
present in the data. To take into account the errors we either include an error
term in the point process model or use an estimation procedure that is robust
with respect to the errors.Comment: 27 pages, 12 figure
Global quantile regression
Quantile regression is used to study effects of covariates on a particular
quantile of the data distribution. Here we are interested in the question
whether a covariate has any effect on the entire data distribution, i.e., on
any of the quantiles. To this end, we treat all the quantiles simultaneously
and consider global tests for the existence of the covariate effect in the
presence of nuisance covariates. This global quantile regression can be used as
the extension of linear regression or as the extension of distribution
comparison in the sense of Kolmogorov-Smirnov test. The proposed method is
based on pointwise coefficients, permutations and global envelope tests. The
global envelope test serves as the multiple test adjustment procedure under the
control of the family-wise error rate and provides the graphical interpretation
which automatically shows the quantiles or the levels of categorical covariate
responsible for the rejection. The Freedman-Lane permutation strategy showed
liberality of the test for extreme quantiles, therefore we propose four
alternatives that work well even for extreme quantiles and are suitable in
different conditions. We present a simulation study to inspect the performance
of these strategies, and we apply the chosen strategies to two data examples.Comment: 44 pages, 12 figure
Tree species, crown cover, and age as determinants of the vertical distribution of airborne LiDAR returns
Light detection and ranging (LiDAR) provides information on the vertical
structure of forest stands enabling detailed and extensive ecosystem study. The
vertical structure is often summarized by scalar features and data-reduction
techniques that limit the interpretation of results. Instead, we quantified the
influence of three variables, species, crown cover, and age, on the vertical
distribution of airborne LiDAR returns from forest stands. We studied 5,428
regular, even-aged stands in Quebec (Canada) with five dominant species: balsam
fir (Abies balsamea (L.) Mill.), paper birch (Betula papyrifera Marsh), black
spruce (Picea mariana (Mill.) BSP), white spruce (Picea glauca Moench) and
aspen (Populus tremuloides Michx.). We modeled the vertical distribution
against the three variables using a functional general linear model and a novel
nonparametric graphical test of significance. Results indicate that LiDAR
returns from aspen stands had the most uniform vertical distribution. Balsam
fir and white birch distributions were similar and centered at around 50% of
the stand height, and black spruce and white spruce distributions were skewed
to below 30% of stand height (p<0.001). Increased crown cover concentrated the
distributions around 50% of stand height. Increasing age gradually shifted the
distributions higher in the stand for stands younger than 70-years, before
plateauing and slowly declining at 90-120 years. Results suggest that the
vertical distributions of LiDAR returns depend on the three variables studied
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