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Abstract The analysis of samples of
curves is a field of growing importance in
Statistics. Samples of curves arise in longitudinal studies, where
random processes are observed on groups of individuals. Often some of
these curves are atypical compared with the rest of the sample, due
either to individual peculiarities or to measurement errors. The most
common techniques for functional data analysis are very sensitive to
outlying curves, which may lead to invalid statistical inference.
Outlier-resistant multivariate techniques are, in most cases, not
directly applicable to functional data, where the number of
observations per curve is usually larger than the sample size.
Therefore, the investigator's goal is to develop robust methods for
functional data analysis that provide valid statistical inference even
in presence of a significant proportion of outlying curves. In
particular, outlier-resistant estimators for the mean and the variance
components are proposed and studied. The properties of these estimators
(such as consistency, asymptotic distribution and breakdown point) are
studied theoretically and empirically, the latter by simulation and
analysis of real datasets. Algorithms and computer software
implementing these methods are being developed.
Examples of functional data are
human growth curves, gene
expression profiles, and daily weather and environmental indicators
(such as precipitation, temperature, pressure, pollution level), to
mention just a few. Thus, detection of atypical growth curves can
provide new insights into the effect of diseases or other unusual
circumstances on human growth, and detection of unusual gene expression
profiles can help understand the genetic causes of abnormal biological
processes or diseases. These examples illustrate the potential for
application of the methods being developed by the investigator to areas
beyond Statistics, such as public health and environmental sciences.
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