9,600 research outputs found
Pitfalls in testing for long run relationships
This paper analyzes the robustness of the two most commonly used cointegration tests: the single equation based test of Engle and Granger (EG) and the system based test of Johansen. We show analytically and numerically several important situations where the Johansen LR tests tend to find spurious cointegration with probability approaching one asymptotically. The situations investigated are of two types. The first one corresponds to variables that have long-memory properties and a trending behavior, but they are not pure I(1) processes although they are difficult to tell from I(1) with standard unit root tests. The second corresponds to I(1) variables whose VAR representation has a singular or near-singular error covariance matrix. In most of the situations investigated in this paper, EG test is more robust than Johansen LR tests. This paper shows that a proper use of the LR test in applied cointegration analysis requires a deeper data analysis than the standard unit root test. We conclude by recommending to use both tests (EG and Johansen) to test for cointegration in order to avoid or to discover a pitfall.Publicad
An analytic comparison of regularization methods for Gaussian Processes
Gaussian Processes (GPs) are a popular approach to predict the output of a
parameterized experiment. They have many applications in the field of Computer
Experiments, in particular to perform sensitivity analysis, adaptive design of
experiments and global optimization. Nearly all of the applications of GPs
require the inversion of a covariance matrix that, in practice, is often
ill-conditioned. Regularization methodologies are then employed with
consequences on the GPs that need to be better understood.The two principal
methods to deal with ill-conditioned covariance matrices are i) pseudoinverse
and ii) adding a positive constant to the diagonal (the so-called nugget
regularization).The first part of this paper provides an algebraic comparison
of PI and nugget regularizations. Redundant points, responsible for covariance
matrix singularity, are defined. It is proven that pseudoinverse
regularization, contrarily to nugget regularization, averages the output values
and makes the variance zero at redundant points. However, pseudoinverse and
nugget regularizations become equivalent as the nugget value vanishes. A
measure for data-model discrepancy is proposed which serves for choosing a
regularization technique.In the second part of the paper, a distribution-wise
GP is introduced that interpolates Gaussian distributions instead of data
points. Distribution-wise GP can be seen as an improved regularization method
for GPs
Principal component analysis and perturbation theory–based robust damage detection of multifunctional aircraft structure
A fundamental problem in structural damage detection is to define an efficient feature to calculate a damage index. Furthermore, due to perturbations from various sources, we also need to define a rigorous threshold whose overtaking indicates the presence of damages. In this article, we develop a robust damage detection methodology based on principal component analysis. We first present an original damage index based on projection of the separation matrix, and then, we drive a novel adaptive threshold that does not rely on statistical assumptions. This threshold is analytic, and it is based on matrix perturbation theory. The efficiency of the method is illustrated using simulations of a composite smart structure and experimental results performed on a conformal load-bearing antenna structure laboratory test
On some limitations of probabilistic models for dimension-reduction: illustration in the case of one particular probabilistic formulation of PLS
Partial Least Squares (PLS) refer to a class of dimension-reduction
techniques aiming at the identification of two sets of components with maximal
covariance, in order to model the relationship between two sets of observed
variables and , with .
El Bouhaddani et al. (2017) have recently proposed a probabilistic formulation
of PLS. Under the constraints they consider for the parameters of their model,
this latter can be seen as a probabilistic formulation of one version of PLS,
namely the PLS-SVD. However, we establish that these constraints are too
restrictive as they define a very particular subset of distributions for
under which, roughly speaking, components with maximal covariance
(solutions of PLS-SVD), are also necessarily of respective maximal variances
(solutions of the principal components analyses of and , respectively).
Then, we propose a simple extension of el Bouhaddani et al.'s model, which
corresponds to a more general probabilistic formulation of PLS-SVD, and which
is no longer restricted to these particular distributions. We present numerical
examples to illustrate the limitations of the original model of el Bouhaddani
et al. (2017)
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