32 research outputs found
Detecting and handling outlying trajectories in irregularly sampled functional datasets
Outlying curves often occur in functional or longitudinal datasets, and can
be very influential on parameter estimators and very hard to detect visually.
In this article we introduce estimators of the mean and the principal
components that are resistant to, and then can be used for detection of,
outlying sample trajectories. The estimators are based on reduced-rank t-models
and are specifically aimed at sparse and irregularly sampled functional data.
The outlier-resistance properties of the estimators and their relative
efficiency for noncontaminated data are studied theoretically and by
simulation. Applications to the analysis of Internet traffic data and glycated
hemoglobin levels in diabetic children are presented.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS257 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Warped Functional Analysis of Variance
This article presents an Analysis of Variance model for functional data that
explicitly incorporates phase variability through a time-warping component,
allowing for a unified approach to estimation and inference in presence of
amplitude and time variability. The focus is on single-random-factor models but
the approach can be easily generalized to more complex ANOVA models. The
behavior of the estimators is studied by simulation, and an application to the
analysis of growth curves of flour beetles is presented. Although the model
assumes a smooth latent process behind the observed trajectories, smoothness of
the observed data is not required; the method can be applied to the sparsely
observed data that is often encountered in longitudinal studies
Outlier detection and trimmed estimation for general functional data
This article introduces trimmed estimators for the mean and covariance
function of general functional data. The estimators are based on a new measure
of outlyingness or data depth that is well defined on any metric space,
although this paper focuses on Euclidean spaces. We compute the breakdown point
of the estimators and show that the optimal breakdown point is attainable for
the appropriate choice of tuning parameters. The small-sample behavior of the
estimators is studied by simulation, and we show that they have better
outlier-resistance properties than alternative estimators. This is confirmed by
two real-data applications, that also show that the outlyingness measure can be
used as a graphical outlier-detection tool in functional spaces where visual
screening of the data is difficult