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Smoothing Splines Estimators in Functional Linear Regression with ErrorsinVariables
, 2006
"... This work deals with a generalization of the Total Least Squares method in the context of the functional linear model. We first propose a smoothing splines estimator of the functional coefficient of the model without noise in the covariates and we obtain an asymptotic result for this estimator. Then ..."
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Cited by 69 (3 self)
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This work deals with a generalization of the Total Least Squares method in the context of the functional linear model. We first propose a smoothing splines estimator of the functional coefficient of the model without noise in the covariates and we obtain an asymptotic result for this estimator. Then, we adapt this estimator to the case where the covariates are noisy and we also derive an upper bound for the convergence speed. Our estimation procedure is evaluated by means of simulations.
Methodology and theory for partial least squares applied to functional data
 Ann. Statist
, 2012
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Asymptotic equivalence of functional linear regression and a white noise inverse problem
 Ann. Statist
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Regularization and Model Selection with Categorial Effect Modifiers
, 2010
"... The case of continuous effect modifiers in varyingcoefficient models has been well investigated. Categorial effect modifiers, however, have been largely neglected. In this paper a regularization technique is proposed that allows for selection of covariates and fusion of categories of categorial ef ..."
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Cited by 2 (0 self)
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The case of continuous effect modifiers in varyingcoefficient models has been well investigated. Categorial effect modifiers, however, have been largely neglected. In this paper a regularization technique is proposed that allows for selection of covariates and fusion of categories of categorial effect modifiers in a linear model. It is distinguished between nominal and ordinal variables, since for the latter more economic parametrizations are warranted. The proposed methods are illustrated and investigated in simulation studies and real world data evaluations. Moreover, some asymptotic properties are derived.
Sparseness and functional data analysis
 The Oxford Handbook of Functional Data Analaysis
, 2010
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Functional Regression of Continuous State Distributions1
"... In this paper we propose a regression model that addresses the problem of distributional relationship between two economic variables. Unlike the classical linear regression, which deals with regressive relationships in the mean only, the proposed model describes and can be used to test on dependence ..."
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Cited by 1 (1 self)
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In this paper we propose a regression model that addresses the problem of distributional relationship between two economic variables. Unlike the classical linear regression, which deals with regressive relationships in the mean only, the proposed model describes and can be used to test on dependence structure between entire distributions. We focus on the case when density functions exist for both left and right hand side variables and are time varying. The case when the variables of interest can be characterized by discrete distributions reduces to traditional vector regression under our framework. Technically, we treat density functions as random elements taking values in the Hilbert spaces of square integrable functions on a compact interval. The regression relationship is described by a compact linear operator mapping from one Hilbert space, where the right hand side density functions reside, to another Hilbert space where left hand side densities reside. We describe how we estimate the model and establish consistency of our estimator. And we develop a hypothesis testing procedure and derive the asymptotic distribution for our test statistic. We investigate finite sample performance of our tests using Monte Carlo simulations. In the end of the paper we offer an empirical illustration of our methodology.
Shape Curve Analysis Using Curvature
, 2009
"... Statistical shape analysis is a field for which there is growing demand. One of the major drivers for this growth is the number of practical applications which can use statistical shape analysis to provide useful insight. An example of one of these practical applications is investigating and compari ..."
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Cited by 1 (0 self)
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Statistical shape analysis is a field for which there is growing demand. One of the major drivers for this growth is the number of practical applications which can use statistical shape analysis to provide useful insight. An example of one of these practical applications is investigating and comparing facial shapes. An ever improving suite of digital imaging technology can capture data on the threedimensional shape of facial features from standard images. A field for which this offers a large amount of potential analytical benefit is the reconstruction of the facial surface of children born with a cleft lip or a cleft lip and palate. This thesis will present two potential methods for analysing data on the facial shape of children who were born with a cleft lip and/or palate using data from two separate studies. One form of analysis will compare the facial shape of one year old children born with a cleft lip and/or palate with the facial shape of control children. The second form of analysis will look for relationships between facial shape and psychological score for ten year old children born with a cleft lip and/or palate. While many of the techniques in this thesis could be extended to
VaryingCoefficient Functional Linear Regression
"... Abstract: Functional linear regression analysis aims to model regression relations which include a functional predictor. The analogue to the regression parameter vector or matrix in conventional multivariate or multipleresponse linear regression models is a regression parameter function in one or t ..."
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Abstract: Functional linear regression analysis aims to model regression relations which include a functional predictor. The analogue to the regression parameter vector or matrix in conventional multivariate or multipleresponse linear regression models is a regression parameter function in one or two arguments. If in addition one has scalar predictors, as is often the case in applications to longitudinal studies, the question arises how to incorporate these into a functional regression model. We study a varyingcoefficient approach where the scalar covariates are modeled as additional arguments of the regression parameter function. This extension of the functional linear regression model is analogous to the extension of conventional linear regression models to varyingcoefficient models, and shares the advantages such as increased flexibility, however the details of this extension are more challenging in the functional case. Our methodology combines smoothing methods with regularization by truncation at a finite number of functional principal components. A practical version is developed and demonstrated to perform better than functional linear regression for longitudinal data. We investigate the asymptotic properties of varyingcoefficient functional linear regression and establish consistency properties.
Varyingcoefficient functional linear
"... Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multipleresponse linear regression models is a regression parameter function in one or two arguments. ..."
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Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multipleresponse linear regression models is a regression parameter function in one or two arguments. If, in addition, one has scalar predictors, as is often the case in applications to longitudinal studies, the question arises how to incorporate these into a functional regression model. We study a varyingcoefficient approach where the scalar covariates are modeled as additional arguments of the regression parameter function. This extension of the functional linear regression model is analogous to the extension of conventional linear regression models to varyingcoefficient models and shares its advantages, such as increased flexibility; however, the details of this extension are more challenging in the functional case. Our methodology combines smoothing methods with regularization by truncation at a finite number of functional principal components. A practical version is developed and is shown to perform better than functional linear regression for longitudinal data. We investigate the asymptotic properties of varyingcoefficient functional linear regression and establish consistency properties.