scholarly journals Spatiotemporal Prediction of COVID-19 Mortality and Risk Assessment

2020 ◽  
Author(s):  
Antoni Torres-Signes ◽  
M. Pilar Frías ◽  
María D.Ruiz-Medina
Keyword(s):  
Mortality Risk ◽  
Functional Data ◽  
Statistical Approach ◽  
Model Fitting ◽  
Functional Regression ◽  
Infinite Dimensional ◽  
Trend Model ◽  
Risk Forecasting ◽  
Model Ranking ◽  
Multivariate Functional Data

Abstract This paper presents a multivariate functional data statistical approach, for spatiotemporal prediction of COVID-19 mortality counts. Specifically, spatial heterogeneous nonlinear parametric functional regression trend model fitting is first implemented. Classical and Bayesian infinite-dimensional log-Gaussian linear residual correlation analysis is then applied. The nonlinear regression predictor of the mortality risk is combined with the plug-in predictor of the multiplicative error term. An empirical model ranking, based on random K-fold validation, is established for COVID-19 mortality risk forecasting and assessment, involving Machine Learning (ML) models, and the adopted Classical and Bayesian semilinear estimation approach. This empirical analysis also determines the ML models favored by the spatial multivariate Functional Data Analysis (FDA) framework. The results could be extrapolated to other countries.

scholarly journals An FDA-Based Approach for Clustering Elicited Expert Knowledge

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 184-204
Author(s):  
Carlos Barrera-Causil ◽  
Juan Carlos Correa ◽  
Andrew Zamecnik ◽  
Francisco Torres-Avilés ◽  
Fernando Marmolejo-Ramos
Keyword(s):  
Functional Data ◽  
Expert Knowledge ◽  
Probability Distributions ◽  
Knowledge Elicitation ◽  
Parallel Analysis ◽  
Data Sets ◽  
Dimensional Problem ◽  
Prior Distributions ◽  
Infinite Dimensional ◽  
Finite Dimensional

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets.

Principal component analysis for functional data

2018 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Principal Component Analysis ◽  
Linear Regression ◽  
Functional Data ◽  
Weighted Least Squares ◽  
Principal Component ◽  
Adaptive Methods ◽  
Component Analysis ◽  
Infinite Dimensional ◽  
Role Of Principal ◽  
Functional Linear Regression

This article discusses the methodology and theory of principal component analysis (PCA) for functional data. It first provides an overview of PCA in the context of finite-dimensional data and infinite-dimensional data, focusing on functional linear regression, before considering the applications of PCA for functional data analysis, principally in cases of dimension reduction. It then describes adaptive methods for prediction and weighted least squares in functional linear regression. It also examines the role of principal components in the assessment of density for functional data, showing how principal component functions are linked to the amount of probability mass contained in a small ball around a given, fixed function, and how this property can be used to define a simple, easily estimable density surrogate. The article concludes by explaining the use of PCA for estimating log-density.

Kernel Regression Estimation for Functional Data

2018 ◽  
Author(s):  
Frédéric Ferraty ◽  
Philippe Vieu
Keyword(s):  
Kernel Methods ◽  
Functional Data ◽  
Linear Functional ◽  
Kernel Smoothing ◽  
Kernel Regression ◽  
Functional Regression ◽  
Regression Estimation ◽  
Asymptotic Results ◽  
Kernel Regression Estimation ◽  
The Impact

This article provides an overview of recent nonparametric and semiparametric advances in kernel regression estimation for functional data. In particular, it considers the various statistical techniques based on kernel smoothing ideas that have recently been developed for functional regression estimation problems. The article first examines nonparametric functional regression modelling before discussing three popular functional regression estimates constructed by means of kernel ideas, namely: the Nadaraya-Watson convolution kernel estimate, the kNN functional estimate, and the local linear functional estimate. Uniform asymptotic results are then presented. The article proceeds by reviewing kernel methods in semiparametric functional regression such as single functional index regression and partial linear functional regression. It also looks at the use of kernels for additive functional regression and concludes by assessing the impact of kernel methods on practical real-data analysis involving functional (curves) datasets.

scholarly journals A functional Hodrick–Prescott filter

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Boualem Djehiche ◽  
Hiba Nassar
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Functional Data ◽  
Separable Hilbert Space ◽  
Underlying Distribution ◽  
Smoothing Operator ◽  
Infinite Dimensional ◽  
Optimal Smoothing ◽  
Functional Version

AbstractWe propose a functional version of the Hodrick–Prescott filter for functional data which take values in an infinite-dimensional separable Hilbert space. We further characterize the associated optimal smoothing operator when the associated linear operator is compact and the underlying distribution of the data is Gaussian.

scholarly journals Clustering multivariate functional data in group-specific functional subspaces

2020 ◽  
Vol 35 (3) ◽  
pp. 1101-1131
Author(s):  
Amandine Schmutz ◽  
Julien Jacques ◽  
Charles Bouveyron ◽  
Laurence Chèze ◽  
Pauline Martin
Keyword(s):  
Functional Data ◽  
Multivariate Functional Data

Operator Geometry in Statistics

2018 ◽  
Author(s):  
Karl Gustafson
Keyword(s):  
Banach Spaces ◽  
Functional Data ◽  
Matrix Inequalities ◽  
Statistical Efficiency ◽  
Prediction Theory ◽  
Geometrical Meaning ◽  
Association Measures ◽  
Canonical Correlations ◽  
Infinite Dimensional ◽  
Two Component

This article discusses the essentials of operator trigonometry developed by the author as it applies to statistics, with emphasis on key elements such as operator antieigenvalues, operator antieigenvectors, and operator turning angles. Operator trigonometry started out infinite dimensional, and remains infinite dimensional, even for Banach spaces. Thus, it is in principle applicable not only to infinite-dimensional statistics but also to cases involving functional data. The article first considers how operator trigonometry gives new geometrical meaning to statistical efficiency before formalizing it in a more deductive manner. It then explains the essentials of operator trigonometry and summarizes the ensuing developments. It also describes two lemmas that are implicit and essential to operator trigonometry, Antieigenvector Reconstruction Lemma and General Two-Component Lemma, and how operator trigonometry provides new geometry to statistics matrix inequalities and canonical correlations. Finally, it presents new results applying operator trigonometry to prediction theory and to association measures.

A statistical approach to schistosome population dynamics and estimation of the life-span of Schistosoma mansoni in man

Parasitology ◽  
1995 ◽  
Vol 110 (3) ◽  
pp. 307-316 ◽  
Author(s):  
A. J. C. Fulford ◽  
A. E. Butterworth ◽  
J. H. Ouma ◽  
R. F. Sturrock
Keyword(s):  
Schistosoma Mansoni ◽  
Life Span ◽  
Statistical Approach ◽  
Dynamic Models ◽  
Model Fitting ◽  
Epidemiological Data ◽  
Host Age ◽  
Force Of Infection ◽  
Data Yield ◽  
And Function

SUMMARYDynamic models which predict changes in the intensity of schistosome infection with host age are fitted to pre-intervention Schistosoma mansoni data from Kenya. Age-specific post-treatment-reinfection data are used to estimate the force of infection, thus enabling investigation of the rate of worm death. An empirical and statistical approach is taken to the model fitting: where possible, distributional properties and function relationships are obtained from the data rather than assumed from theory. Attempts are made to remove known sources of bias. Maximum likelihood techniques, employed to allow for error in both the pre-intervention and reinfection data, yield confidence intervals for the worm life-span (CI95% = 5·7–10·5 years) and demonstrate that the worm death rate is unlikely to vary with host age. The possibilities and limitations of fitting dynamic models to data are discussed. We conclude that a detailed, quantitative approach will be necessary if progress is to be made with the interpretation of epidemiological data and the models intended to describe them.

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