3,280 research outputs found
Variable selection in measurement error models
Measurement error data or errors-in-variable data have been collected in many
studies. Natural criterion functions are often unavailable for general
functional measurement error models due to the lack of information on the
distribution of the unobservable covariates. Typically, the parameter
estimation is via solving estimating equations. In addition, the construction
of such estimating equations routinely requires solving integral equations,
hence the computation is often much more intensive compared with ordinary
regression models. Because of these difficulties, traditional best subset
variable selection procedures are not applicable, and in the measurement error
model context, variable selection remains an unsolved issue. In this paper, we
develop a framework for variable selection in measurement error models via
penalized estimating equations. We first propose a class of selection
procedures for general parametric measurement error models and for general
semi-parametric measurement error models, and study the asymptotic properties
of the proposed procedures. Then, under certain regularity conditions and with
a properly chosen regularization parameter, we demonstrate that the proposed
procedure performs as well as an oracle procedure. We assess the finite sample
performance via Monte Carlo simulation studies and illustrate the proposed
methodology through the empirical analysis of a familiar data set.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ205 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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
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Robust variable selection in partially varying coefficient single-index model
By combining basis function approximations and smoothly clipped absolute deviation (SCAD) penalty, this paper proposes a robust variable selection procedure for a partially varying coefficient single-index model based on modal regression. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation. Furthermore, we also discuss the bandwidth selection and propose a modified expectation-maximization (EM)-type algorithm for the proposed estimation procedure. The finite sample properties of the proposed estimators are illustrated by some simulation examples.The research of Zhu is partially supported by National Natural Science Foundation of China (NNSFC) under Grants 71171075, 71221001 and 71031004. The research of Yu is supported by NNSFC under Grant 11261048
IGS: an IsoGeometric approach for Smoothing on surfaces
We propose an Isogeometric approach for smoothing on surfaces, namely
estimating a function starting from noisy and discrete measurements. More
precisely, we aim at estimating functions lying on a surface represented by
NURBS, which are geometrical representations commonly used in industrial
applications. The estimation is based on the minimization of a penalized
least-square functional. The latter is equivalent to solve a 4th-order Partial
Differential Equation (PDE). In this context, we use Isogeometric Analysis
(IGA) for the numerical approximation of such surface PDE, leading to an
IsoGeometric Smoothing (IGS) method for fitting data spatially distributed on a
surface. Indeed, IGA facilitates encapsulating the exact geometrical
representation of the surface in the analysis and also allows the use of at
least globally continuous NURBS basis functions for which the 4th-order
PDE can be solved using the standard Galerkin method. We show the performance
of the proposed IGS method by means of numerical simulations and we apply it to
the estimation of the pressure coefficient, and associated aerodynamic force on
a winglet of the SOAR space shuttle
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