119,078 research outputs found
Robust functional regression based on principal components
Functional data analysis is a fast evolving branch of modern statistics and
the functional linear model has become popular in recent years. However, most
estimation methods for this model rely on generalized least squares procedures
and therefore are sensitive to atypical observations. To remedy this, we
propose a two-step estimation procedure that combines robust functional
principal components and robust linear regression. Moreover, we propose a
transformation that reduces the curvature of the estimators and can be
advantageous in many settings. For these estimators we prove Fisher-consistency
at elliptical distributions and consistency under mild regularity conditions.
The influence function of the estimators is investigated as well. Simulation
experiments show that the proposed estimators have reasonable efficiency,
protect against outlying observations, produce smooth estimates and perform
well in comparison to existing approaches.Comment: 33 pages, including the appendix and reference
Intraday forecasts of a volatility index: Functional time series methods with dynamic updating
As a forward-looking measure of future equity market volatility, the VIX
index has gained immense popularity in recent years to become a key measure of
risk for market analysts and academics. We consider discrete reported intraday
VIX tick values as realisations of a collection of curves observed sequentially
on equally spaced and dense grids over time and utilise functional data
analysis techniques to produce one-day-ahead forecasts of these curves. The
proposed method facilitates the investigation of dynamic changes in the index
over very short time intervals as showcased using the 15-second high-frequency
VIX index values. With the help of dynamic updating techniques, our point and
interval forecasts are shown to enjoy improved accuracy over conventional time
series models.Comment: 29 pages, 5 figures, To appear at the Annals of Operations Researc
Robust regularized singular value decomposition with application to mortality data
We develop a robust regularized singular value decomposition (RobRSVD) method
for analyzing two-way functional data. The research is motivated by the
application of modeling human mortality as a smooth two-way function of age
group and year. The RobRSVD is formulated as a penalized loss minimization
problem where a robust loss function is used to measure the reconstruction
error of a low-rank matrix approximation of the data, and an appropriately
defined two-way roughness penalty function is used to ensure smoothness along
each of the two functional domains. By viewing the minimization problem as two
conditional regularized robust regressions, we develop a fast iterative
reweighted least squares algorithm to implement the method. Our implementation
naturally incorporates missing values. Furthermore, our formulation allows
rigorous derivation of leave-one-row/column-out cross-validation and
generalized cross-validation criteria, which enable computationally efficient
data-driven penalty parameter selection. The advantages of the new robust
method over nonrobust ones are shown via extensive simulation studies and the
mortality rate application.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS649 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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