Semi-functional partial linear regression

Aneiros, Germán; Vieu, Philippe

doi:10.1016/j.spl.2005.12.007

Cited by 184 publications

(119 citation statements)

References 9 publications

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“…report even better RMSE (0.34) for another Bayesian neural network method [7]. The RMSE of our method is 0.43 (LS-SVM with scaling), which is better than the results reported in [8], [10] and [9].…”

Section: Resultscontrasting

confidence: 46%

Gaussian Fitting Based FDA for Chemometrics

Kärnä

Lendasse

Computational and Ambient Intelligence

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Abstract. In Functional Data Analysis (FDA) multivariate data are considered as sampled functions. We propose a non-supervised method for finding a good function basis that is built on the data set. The basis consists of a set of Gaussian kernels that are optimized for an accurate fitting. The proposed methodology is experimented with two spectrometric data sets. The obtained weights are further scaled using a Delta Test (DT) to improve the prediction performance. Least Squares Support Vector Machine (LS-SVM) model is used for estimation.

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Section: Resultscontrasting

confidence: 46%

Gaussian Fitting Based FDA for Chemometrics

Kärnä

Lendasse

Computational and Ambient Intelligence

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“…In this analysis, is the fat content, { } are functional principal component (FPC) scores of ( ), and = Ψ( , ), we take the protein and the moisture content by 1 and 2 , respectively. In order to predict the fat content of a meat sample, many models and algorithms are proposed to fit the data; see, for example, Aneiros-Pérez and Vieu [26]. In this paper, to fit the data, we consider the following partially linear functional additive model:…”

Section: Application To Real Datamentioning

confidence: 99%

Automatic Variable Selection for Partially Linear Functional Additive Model and Its Application to the Tecator Data Set

Feng

Xue

2018

Mathematical Problems in Engineering

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We introduce a new partially linear functional additive model, and we consider the problem of variable selection for this model. Based on the functional principal components method and the centered spline basis function approximation, a new variable selection procedure is proposed by using the smooth-threshold estimating equation (SEE). The proposed procedure automatically eliminates inactive predictors by setting the corresponding parameters to be zero and simultaneously estimates the nonzero regression coefficients by solving the SEE. The approach avoids the convex optimization problem, and it is flexible and easy to implement. We establish the asymptotic properties of the resulting estimators under some regularity conditions. We apply the proposed procedure to analyze a real data set: the Tecator data set.

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“…In this session, as the motivation of our proposal, we first review the PLS basis in model (1) where both information of the functional covariates and the responses are used to choose the basis functions. Then we propose our developed methodology to choose basis for model (2), namely, partial quantile regression (PQR) basis.…”

Section: Partial Functional Linear Quantile Regressionmentioning

confidence: 99%

“…In the existing literature, model (2) has been well studied and various methods have been proposed. As in functional linear regression, to estimate functional coefficients γ τ (t) it is convenient to restrict it in a functional space with a finite basis.…”

Section: Introductionmentioning

confidence: 99%

Partial functional linear quantile regression for neuroimaging data analysis

Kong

Mizera

2016

Neurocomputing

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We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial quantile regression (PQR) basis for estimating functional coefficients. We further extend our partial quantile covariance techniques to functional composite quantile regression (CQR) defining partial composite quantile covariance. There are three major contributions. (1) We define partial quantile covariance between two scalar variables through linear quantile regression. We compute PQR basis by sequentially maximizing the partial quantile covariance between the response and projections of functional covariates. (2) In order to efficiently extract PQR basis, we develop a SIMPQR algorithm analogous to simple partial least squares (SIMPLS). (3) Under the homoscedasticity assumption, we extend our techniques to partial composite quantile covariance and use it to find the partial composite quantile regression (PCQR) basis. The SIMPQR algorithm is then modified to obtain the SIMPCQR algorithm. Two simulation studies show the superiority of our * Corresponding author Email address: lkong@ualberta.ca (Linglong Kong) 1 Part of the data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.ucla.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.ucla.edu/wp-content/ uploads/how to apply/ADNI Acknowledgement List.pdf proposed methods. Two real data from ADHD-200 sample and ADNI are analyzed using our proposed methods.

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Semi-functional partial linear regression

Cited by 184 publications

References 9 publications

Gaussian Fitting Based FDA for Chemometrics

Gaussian Fitting Based FDA for Chemometrics

Automatic Variable Selection for Partially Linear Functional Additive Model and Its Application to the Tecator Data Set

Partial functional linear quantile regression for neuroimaging data analysis

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