3,775 research outputs found
An Automated Approach Towards Sparse Single-Equation Cointegration Modelling
In this paper we propose the Single-equation Penalized Error Correction
Selector (SPECS) as an automated estimation procedure for dynamic
single-equation models with a large number of potentially (co)integrated
variables. By extending the classical single-equation error correction model,
SPECS enables the researcher to model large cointegrated datasets without
necessitating any form of pre-testing for the order of integration or
cointegrating rank. Under an asymptotic regime in which both the number of
parameters and time series observations jointly diverge to infinity, we show
that SPECS is able to consistently estimate an appropriate linear combination
of the cointegrating vectors that may occur in the underlying DGP. In addition,
SPECS is shown to enable the correct recovery of sparsity patterns in the
parameter space and to posses the same limiting distribution as the OLS oracle
procedure. A simulation study shows strong selective capabilities, as well as
superior predictive performance in the context of nowcasting compared to
high-dimensional models that ignore cointegration. An empirical application to
nowcasting Dutch unemployment rates using Google Trends confirms the strong
practical performance of our procedure
Penalized Likelihood and Bayesian Function Selection in Regression Models
Challenging research in various fields has driven a wide range of
methodological advances in variable selection for regression models with
high-dimensional predictors. In comparison, selection of nonlinear functions in
models with additive predictors has been considered only more recently. Several
competing suggestions have been developed at about the same time and often do
not refer to each other. This article provides a state-of-the-art review on
function selection, focusing on penalized likelihood and Bayesian concepts,
relating various approaches to each other in a unified framework. In an
empirical comparison, also including boosting, we evaluate several methods
through applications to simulated and real data, thereby providing some
guidance on their performance in practice
Statistical Compressed Sensing of Gaussian Mixture Models
A novel framework of compressed sensing, namely statistical compressed
sensing (SCS), that aims at efficiently sampling a collection of signals that
follow a statistical distribution, and achieving accurate reconstruction on
average, is introduced. SCS based on Gaussian models is investigated in depth.
For signals that follow a single Gaussian model, with Gaussian or Bernoulli
sensing matrices of O(k) measurements, considerably smaller than the O(k
log(N/k)) required by conventional CS based on sparse models, where N is the
signal dimension, and with an optimal decoder implemented via linear filtering,
significantly faster than the pursuit decoders applied in conventional CS, the
error of SCS is shown tightly upper bounded by a constant times the best k-term
approximation error, with overwhelming probability. The failure probability is
also significantly smaller than that of conventional sparsity-oriented CS.
Stronger yet simpler results further show that for any sensing matrix, the
error of Gaussian SCS is upper bounded by a constant times the best k-term
approximation with probability one, and the bound constant can be efficiently
calculated. For Gaussian mixture models (GMMs), that assume multiple Gaussian
distributions and that each signal follows one of them with an unknown index, a
piecewise linear estimator is introduced to decode SCS. The accuracy of model
selection, at the heart of the piecewise linear decoder, is analyzed in terms
of the properties of the Gaussian distributions and the number of sensing
measurements. A maximum a posteriori expectation-maximization algorithm that
iteratively estimates the Gaussian models parameters, the signals model
selection, and decodes the signals, is presented for GMM-based SCS. In real
image sensing applications, GMM-based SCS is shown to lead to improved results
compared to conventional CS, at a considerably lower computational cost
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