32,769 research outputs found
Projection-based nonparametric goodness-of-fit testing with functional covariates
This paper studies the problem of nonparametric testing for the effect of a
random functional covariate on a real-valued error term. The covariate takes
values in , the Hilbert space of the square-integrable real-valued
functions on the unit interval. The error term could be directly observed as a
response or \emph{estimated} from a functional parametric model, like for
instance the functional linear regression. Our test is based on the remark that
checking the no-effect of the functional covariate is equivalent to checking
the nullity of the conditional expectation of the error term given a
sufficiently rich set of projections of the covariate. Such projections could
be on elements of norm 1 from finite-dimension subspaces of . Next,
the idea is to search a finite-dimension element of norm 1 that is, in some
sense, the least favorable for the null hypothesis. Finally, it remains to
perform a nonparametric check of the nullity of the conditional expectation of
the error term given the scalar product between the covariate and the selected
least favorable direction. For such finite-dimension search and nonparametric
check we use a kernel-based approach. As a result, our test statistic is a
quadratic form based on univariate kernel smoothing and the asymptotic critical
values are given by the standard normal law. The test is able to detect
nonparametric alternatives, including the polynomial ones. The error term could
present heteroscedasticity of unknown form. We do no require the law of the
covariate to be known. The test could be implemented quite easily and
performs well in simulations and real data applications. We illustrate the
performance of our test for checking the functional linear regression model
Data-driven and Model-based Verification: a Bayesian Identification Approach
This work develops a measurement-driven and model-based formal verification
approach, applicable to systems with partly unknown dynamics. We provide a
principled method, grounded on reachability analysis and on Bayesian inference,
to compute the confidence that a physical system driven by external inputs and
accessed under noisy measurements, verifies a temporal logic property. A case
study is discussed, where we investigate the bounded- and unbounded-time safety
of a partly unknown linear time invariant system
Nonparametric checks for single-index models
In this paper we study goodness-of-fit testing of single-index models. The
large sample behavior of certain score-type test statistics is investigated. As
a by-product, we obtain asymptotically distribution-free maximin tests for a
large class of local alternatives. Furthermore, characteristic function based
goodness-of-fit tests are proposed which are omnibus and able to detect peak
alternatives. Simulation results indicate that the approximation through the
limit distribution is acceptable already for moderate sample sizes.
Applications to two real data sets are illustrated.Comment: Published at http://dx.doi.org/10.1214/009053605000000020 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Theoretically Guaranteed Deep Optimization Framework for Robust Compressive Sensing MRI
Magnetic Resonance Imaging (MRI) is one of the most dynamic and safe imaging
techniques available for clinical applications. However, the rather slow speed
of MRI acquisitions limits the patient throughput and potential indi cations.
Compressive Sensing (CS) has proven to be an efficient technique for
accelerating MRI acquisition. The most widely used CS-MRI model, founded on the
premise of reconstructing an image from an incompletely filled k-space, leads
to an ill-posed inverse problem. In the past years, lots of efforts have been
made to efficiently optimize the CS-MRI model. Inspired by deep learning
techniques, some preliminary works have tried to incorporate deep architectures
into CS-MRI process. Unfortunately, the convergence issues (due to the
experience-based networks) and the robustness (i.e., lack real-world noise
modeling) of these deeply trained optimization methods are still missing. In
this work, we develop a new paradigm to integrate designed numerical solvers
and the data-driven architectures for CS-MRI. By introducing an optimal
condition checking mechanism, we can successfully prove the convergence of our
established deep CS-MRI optimization scheme. Furthermore, we explicitly
formulate the Rician noise distributions within our framework and obtain an
extended CS-MRI network to handle the real-world nosies in the MRI process.
Extensive experimental results verify that the proposed paradigm outperforms
the existing state-of-the-art techniques both in reconstruction accuracy and
efficiency as well as robustness to noises in real scene
Consistent tests of conditional moment restrictions
We propose two classes of consistent tests in parametric econometric models defined through multiple conditional moment restrictions. The first type of tests relies on nonparametric estimation, while the second relies on a functional of a marked empirical process. For both tests, a simulation procedure for obtaining critical values is shown to be asymptotically valid. Finite sample performances of the tests are investigated by means of several Monte-Carlo experiments.Publicad
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