1,559 research outputs found
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Necklace-Cloverleaf Transition in Associating RNA-like Diblock Copolymers
We consider a diblock copolymer, whose links are capable
of forming local reversible bonds with each other. We assume that the resulting
structure of the bonds is RNA--like, i.e. topologically isomorphic to a tree.
We show that, depending on the relative strengths of A--A, A--B and B--B
contacts, such a polymer can be in one of two different states. Namely, if a
self--association is preferable (i.e., A--A and B--B bonds are comparatively
stronger than A--B contacts) then the polymer forms a typical randomly branched
cloverleaf structure. On the contrary, if alternating association is preferable
(i.e. A--B bonds are stronger than A--A and B--B contacts) then the polymer
tends to form a generally linear necklace structure (with, probably, some rear
side branches and loops, which do not influence the overall characteristics of
the chain). The transition between cloverleaf and necklace states is studied in
details and it is shown that it is a 2nd order phase transition.Comment: 17 pages, 9 figure
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
Generalized Spatial Regression with Differential Regularization
We aim at analyzing geostatistical and areal data observed over irregularly
shaped spatial domains and having a distribution within the exponential family.
We propose a generalized additive model that allows to account for
spatially-varying covariate information. The model is fitted by maximizing a
penalized log-likelihood function, with a roughness penalty term that involves
a differential quantity of the spatial field, computed over the domain of
interest. Efficient estimation of the spatial field is achieved resorting to
the finite element method, which provides a basis for piecewise polynomial
surfaces. The proposed model is illustrated by an application to the study of
criminality in the city of Portland, Oregon, USA
Nonparametric tests for semiparametric regression models
Semiparametric regression models have received considerable attention over the last decades, because of their flexibility and their good finite sample performances. Here we propose an innovative nonparametric test for the linear part of the models, based on random sign-flipping of an appropriate transformation of the residuals, that exploits a spectral decomposition of the residualizing matrix associated with the nonparametric part of the model. The test can be applied to a vast class of extensively used semiparametric regression models with roughness penalties, with nonparametric components defined over one-dimensional, as well as over multi-dimensional domains, including, for instance, models based on univariate or multivariate splines. We prove the good asymptotic properties of the proposed test. Moreover, by means of extensive simulation studies, we show the superiority of the proposed test with respect to current parametric alternatives, demonstrating its excellent control of the Type I error, accompanied by a good power, even in challenging data scenarios, where instead current parametric alternatives fail
Observation of vortex-nucleated magnetization reversal in individual ferromagnetic nanotubes
The reversal of a uniform axial magnetization in a ferromagnetic nanotube
(FNT) has been predicted to nucleate and propagate through vortex domains
forming at the ends. In dynamic cantilever magnetometry measurements of
individual FNTs, we identify the entry of these vortices as a function of
applied magnetic field and show that they mark the nucleation of magnetization
reversal. We find that the entry field depends sensitively on the angle between
the end surface of the FNT and the applied field. Micromagnetic simulations
substantiate the experimental results and highlight the importance of the ends
in determining the reversal process. The control over end vortex formation
enabled by our findings is promising for the production of FNTs with tailored
reversal properties.Comment: 20 pages, 13 figure
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