Functional convolution models

@article{Asencio2014FunctionalCM,
  title={Functional convolution models},
  author={Maria Asencio and Giles Hooker and H. Oliver Gao},
  journal={Statistical Modelling},
  year={2014},
  volume={14},
  pages={315 - 335}
}
This article considers the application of functional data analysis methods to modelling particulate matter emission profiles from dynamometer experiments. In particular the functional convolution model is introduced as an extension of the distributed lag model to functional (smooth and continuous) observations. We present a penalized ordinary least squares estimator for the model and a novel bootstrap procedure to provide pointwise confidence regions for the estimated convolution functions. The… Expand

Figures from this paper

On the Identifiability of the Functional Convolution Model
This report details conditions under which the Functional Convolution Model described in \citet{AHG13} can be identified from Ordinary Least Squares estimates without either dimension reduction orExpand
Estimation in Functional Convolution Model
The aim of the paper is to propose an estimator of the unknown function in the Functional Convolution Model (FCVM), which studies the relationship between a functional covariate X(t) and a functionalExpand
Truncated linear models for functional data
Summary A conventional linear model for functional data involves expressing a response variable Y in terms of the explanatory function X(t), via the model , where a is a scalar, b is an unknownExpand
Sparse Estimation of Historical Functional Linear Models with a Nested Group Bridge Approach
The conventional historical functional linear model relates the current value of the functional response at time t to all past values of the functional covariate up to time t. Motivated by situationsExpand
Estimating Truncated Functional Linear Models With a Nested Group Bridge Approach
Abstract We study a scalar-on-function truncated linear regression model which assumes that the functional predictor does not influence the response when the time passes a certain cutoff point. WeExpand
A Functional Data Method for Causal Dynamic Network Modeling of Task-Related fMRI
TLDR
This paper proposes a causal dynamic network (CDN) method to estimate brain activations and connections simultaneously in fMRI, which achieves higher estimation accuracy while improving the computational speed by from tens to thousands of times. Expand
Restricted likelihood ratio tests for linearity in scalar-on-function regression
TLDR
This work proposes a procedure for testing the linearity of a scalar-on-function regression relationship and shows how the functional linear model can be represented as a simple mixed model nested within the FGAM, a recently developed extension of thefunctional linear model. Expand
Asymptotic analysis of microtubule-based transport by multiple identical molecular motors.
TLDR
Through an asymptotic analysis of a system of SDEs, a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo is developed to make analytical predictions for two parameter regimes that have thus far eluded direct experimental observation. Expand
Functional linear regression models : application to high-throughput plant phenotyping functional data
L'Analyse des Donnees Fonctionnelles (ADF) est une branche de la statistique qui est de plus en plus utilisee dans de nombreux domaines scientifiques appliques tels que l'experimentation biologique,Expand

References

SHOWING 1-10 OF 35 REFERENCES
On the Identifiability of the Functional Convolution Model
This report details conditions under which the Functional Convolution Model described in \citet{AHG13} can be identified from Ordinary Least Squares estimates without either dimension reduction orExpand
The historical functional linear model
The authors develop a functional linear model in which the values at time t of a sample of curves yi (t) are explained in a feed-forward sense by the values of covariate curves xi(s) observed atExpand
Functional Data Analysis
  • H. Müller
  • Computer Science
  • International Encyclopedia of Statistical Science
  • 2011
TLDR
An overview of FDA is provided, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is Functional Principal Component Analysis (FPCA), an important dimension reduction tool and in sparse data situations can be used to impute functional data that are sparsely observed. Expand
A statistical model of vehicle emissions and fuel consumption
Many vehicle emission models am overly simple, such as the speed dependent models used widely, and other models are sufficiently complicated as to require excessive inputs and calculations, which canExpand
Towards accurate instantaneous emission models
Abstract To address the needs of researchers and policy makers on local levels, a microscopic (i.e. at vehicle level) instantaneous emission model is being developed. This model aims to predictExpand
Resampling Methods for Dependent Data
TLDR
This book presents recent developments in Bayesian nonlinear modeling and provides a complete treatment of regression and classiŽ cation problems by emphasizing a data-driven approach in determining appropriate models. Expand
A comparative study of one-level and two-level semiparametric estimation of hemodynamic response function for fMRI data.
TLDR
A semiparametric approach is developed, based on the cubic smoothing splines, to obtain statistically more efficient estimates of the underlying hemodynamic response function (HRF) associated with fMRI experiments to identify the brain regions which are activated when a subject performs a particular task. Expand
The concentration-response relation between PM(2.5) and daily deaths.
TLDR
The magnitude of the association suggests that controlling fine particle pollution would result in thousands of fewer early deaths per year, and an essentially linear relationship down to 2 microg/m(3). Expand
Bootstrap Methods For Time Series
The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data. The methods that are available forExpand
A Bayesian Time-Course Model for Functional Magnetic Resonance Imaging Data
TLDR
A nonlinear Bayesian hierarchical model for fMRI data is described and inferential methods that enable investigators to directly target their scientific questions of interest, many of which are inaccessible to current methods are presented. Expand
...
1
2
3
4
...