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Coefficient Functions (coefficient + function)

Distribution by Scientific Domains
Mathematics and Statistics66%
Engineering33%

Selected Abstracts

Functional Generalized Linear Models with Images as Predictors

BIOMETRICS, Issue 1 2010
Philip T. Reiss
Summary Functional principal component regression (FPCR) is a promising new method for regressing scalar outcomes on functional predictors. In this article, we present a theoretical justification for the use of principal components in functional regression. FPCR is then extended in two directions: from linear to the generalized linear modeling, and from univariate signal predictors to high-resolution image predictors. We show how to implement the method efficiently by adapting generalized additive model technology to the functional regression context. A technique is proposed for estimating simultaneous confidence bands for the coefficient function; in the neuroimaging setting, this yields a novel means to identify brain regions that are associated with a clinical outcome. A new application of likelihood ratio testing is described for assessing the null hypothesis of a constant coefficient function. The performance of the methodology is illustrated via simulations and real data analyses with positron emission tomography images as predictors. [source]

Identification of Time-Variant Modal Parameters Using Time-Varying Autoregressive with Exogenous Input and Low-Order Polynomial Function

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 7 2009
C. S. Huang
By developing the equivalent relations between the equation of motion of a time-varying structural system and the TVARX model, this work proves that instantaneous modal parameters of a time-varying system can be directly estimated from the TVARX model coefficients established from displacement responses. A moving least-squares technique incorporating polynomial basis functions is adopted to approximate the coefficient functions of the TVARX model. The coefficient functions of the TVARX model are represented by polynomials having time-dependent coefficients, instead of constant coefficients as in traditional basis function expansion approaches, so that only low orders of polynomial basis functions are needed. Numerical studies are carried out to investigate the effects of parameters in the proposed approach on accurately determining instantaneous modal parameters. Numerical analyses also demonstrate that the proposed approach is superior to some published techniques (i.e., recursive technique with a forgetting factor, traditional basis function expansion approach, and weighted basis function expansion approach) in accurately estimating instantaneous modal parameters of a structure. Finally, the proposed approach is applied to process measured data for a frame specimen subjected to a series of base excitations in shaking table tests. The specimen was damaged during testing. The identified instantaneous modal parameters are consistent with observed physical phenomena. [source]

Uniform asymptotic Green's functions for efficient modeling of cracks in elastic layers with relative shear deformation controlled by linear springs

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2009
Anthony P. Peirce
Abstract We present a uniform asymptotic solution (UAS) for a displacement discontinuity (DD) that lies within the middle layer of a three-layer elastic medium in which relative shear deformation between parallel interfaces is controlled by linear springs. The DD is assumed to be normal to the two interfaces between the elastic media. Using the Fourier transform method we construct a leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three-layer-spring medium. Although a closed-form solution will require a solution in terms of an infinite series, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We compare the results using the Green's function UAS solution for a crack crossing a soft interface with results obtained using a multi-layer boundary element method. We also present results from an implementation of the UAS Green's function approach in a pseudo-3D hydraulic fracturing simulator to analyze the effect of interface shear deformation on the fracture propagation process. These results are compared with field measurements. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Functional Coefficient Autoregressive Models: Estimation and Tests of Hypotheses

JOURNAL OF TIME SERIES ANALYSIS, Issue 2 2001
Rong Chen
In this paper, we study nonparametric estimation and hypothesis testing procedures for the functional coefficient AR (FAR) models of the form Xt=f1(Xt,d)Xt, 1+ ... +fp(Xt,d)Xt,p+,t, first proposed by Chen and Tsay (1993). As a direct generalization of the linear AR model, the FAR model is a rich class of models that includes many useful parametric nonlinear time series models such as the threshold AR models of Tong (1983) and exponential AR models of Haggan and Ozaki (1981). We propose a local linear estimation procedure for estimating the coefficient functions and study its asymptotic properties. In addition, we propose two testing procedures. The first one tests whether all the coefficient functions are constant, i.e. whether the process is linear. The second one tests if all the coefficient functions are continuous, i.e. if any threshold type of nonlinearity presents in the process. The results of some simulation studies as well as a real example are presented. [source]

Corrected local polynomial estimation in varying-coefficient models with measurement errors

THE CANADIAN JOURNAL OF STATISTICS, Issue 3 2006
Jinhong You
Abstract The authors study a varying-coefficient regression model in which some of the covariates are measured with additive errors. They find that the usual local linear estimator (LLE) of the coefficient functions is biased and that the usual correction for attenuation fails to work. They propose a corrected LLE and show that it is consistent and asymptotically normal, and they also construct a consistent estimator for the model error variance. They then extend the generalized likelihood technique to develop a goodness of fit test for the model. They evaluate these various procedures through simulation studies and use them to analyze data from the Framingham Heart Study. Estimation polynomiale locale corrigée dans les modèles à coefficients variables comportant des erreurs de mesure Les auteurs s'intéressent à un modèle de régression à coefficients variables dont certaines cova-riables sont entachées d'erreurs additives. Ils montrent que l'estimateur localement linéaire (ELL) usuel des coefficients fonctionnels est biaisé et que le facteur de correction habituel du phénomène d'atténuation est inefficace. Ils proposent une version corrigée de l'ELL qui s'avère convergente et asymptotiquement normale; ils suggèrent aussi une estimation convergente de la variance du terme d'erreur du modèle. Une adaptation de la technique de vraisemblance généralisée leur permet en outre d'élaborer un test d'adéquation du modèle. Ils évaluent ces diverses procédures par voie de simulation et s'en servent pour analyser des données issues de l'étude Framingham sur les risques cardiométaboliques. [source]