ArticleElectronic journal of statistics2012
Structured penalties for functional linear models-partially empirical eigenvectors for regression.
Article in Electronic journal of statistics, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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Who cites it
13 citing papers in PubMed.
- Incorporation of spatial- and connectivity-based cortical brain region information in regularized regression: Application to Human Connectome Project data.Frontiers in neuroscience · 2022Article
- Ridge Penalization in High-Dimensional Testing With Applications to Imaging Genetics.Frontiers in neuroscience · 2022Article
- Connectivity-informed adaptive regularization for generalized outcomes.The Canadian journal of statistics = Revue canadienne de statistique · 2021Article
- Use of Functional Linear Models to Detect Associations between Characteristics of Walking and Continuous Responses Using Accelerometry Data.Sensors (Basel, Switzerland) · 2020Article
- Brain connectivity-informed regularization methods for regression.Statistics in biosciences · 2019Article
- A joint design for functional data with application to scheduling ultrasound scans.Computational statistics & data analysis · 2018Article
- KERNEL-PENALIZED REGRESSION FOR ANALYSIS OF MICROBIOME DATA.The annals of applied statistics · 2018Article
- Methods for scalar-on-function regression.International statistical review = Revue internationale de statistique · 2017Article
- Adaptive penalties for generalized Tikhonov regularization in statistical regression models with application to spectroscopy data.Journal of chemometrics · 2017Article
- Penalized nonparametric scalar-on-function regression via principal coordinates.Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America · 2017Article
- Prediction of Intravenous Busulfan Clearance by Endogenous Plasma Biomarkers Using Global Pharmacometabolomics.Metabolomics : Official journal of the Metabolomic Society · 2016Article
- A significance test for graph-constrained estimation.Biometrics · 2016Article
- Longitudinal Functional Models with Structured Penalties.Statistical modelling · 2016Article
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Authors and funding
3 authors.
Funding
Abstract
One of the challenges with functional data is incorporating geometric structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear model is often used to estimate the relationship between the predictor functions and scalar responses. Common approaches to the problem of estimating a coefficient function typically involve two stages: regularization and estimation. Regularization is usually done via dimension reduction, projecting onto a predefined span of basis functions or a reduced set of eigenvectors (principal components). In contrast, we present a unified approach that directly incorporates geometric structure into the estimation process by exploiting the joint eigenproperties of the predictors and a linear penalty operator. In this sense, the components in the regression are 'partially empirical' and the framework is provided by the generalized singular value decomposition (GSVD). The form of the penalized estimation is not new, but the GSVD clarifies the process and informs the choice of penalty by making explicit the joint influence of the penalty and predictors on the bias, variance and performance of the estimated coefficient function. Laboratory spectroscopy data and simulations are used to illustrate the concepts.
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Registered trials
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