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Simultaneous Confidence Band for Stationary Covariance Function of Dense Functional Data
[article]
2019
arXiv
pre-print
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Inference via simultaneous confidence band is studied for stationary covariance function of dense functional data. ...
An asymptotic simultaneous confidence band (SCB) is developed for the true covariance function, and the coverage probabilities are shown to be asymptotically correct. ...
In this sense, Cao et al. (2016) proposed a simultaneous confidence envelope of covariance function for functional data; Horváth et al. (2013) proposed a consistent estimator for the long-run covariance ...
arXiv:1903.05522v3
fatcat:s3aetouxhfdq3pgk66tnfrth5a
BFDA: A MATLAB Toolbox for Bayesian Functional Data Analysis
2019
Journal of Statistical Software
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functional data with stationary and nonstationary covariance functions, and without the requirement of common observation grids; (3) provides accurately smoothed functional data for follow-up analysis ...
The advantages of BFDA include: (1) simultaneously smooths multiple functional data samples and estimates the mean-covariance functions in a nonparametric way; (2) flexibly deals with sparse and high-dimensional ...
Examples are provided in the supplementary file about using the fdaM package with functional data smoothed by BFDA. Details about the inputs and outputs of BFDA are provided in Appendix A. ...
doi:10.18637/jss.v089.i02
fatcat:wjoctmyh35dhhnpfk2srp72gm4
BFDA: A Matlab Toolbox for Bayesian Functional Data Analysis
[article]
2017
arXiv
pre-print
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functional data with stationary and nonstationary covariance functions, and without the requirement of common observation grids; (3) provides accurately smoothed functional data for follow-up analysis ...
The advantages of BFDA include: (1) Simultaneously smooths multiple functional data and estimates the mean-covariance functions in a nonparametric way; (2) flexibly deals with sparse and high-dimensional ...
Moreover, BFDA is flexible for analyzing sparse and dense functional data without the requirement of common observation grids, suitable for analyzing functional data with both stationary and nonstationary ...
arXiv:1604.05224v2
fatcat:6gwwce35vvhfbevradu56wtkna
Oracle-Efficient Confidence Envelopes for Covariance Functions in Dense Functional Data
2017
Statistica sinica
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We consider nonparametric estimation of the covariance function for dense functional data using computationally efficient tensor product B-splines. ...
Simultaneous confidence envelopes are developed based on asymptotic theory to quantify the variability in the covariance estimator and to make global inferences on the true covariance. ...
We show the estimated covariance function and Using the simultaneous confidence envelopes, one can test other interesting hypotheses on the true covariance function, such as the true covariance being stationary ...
doi:10.5705/ss.2014.182
fatcat:3dkjda7bo5fwlitfgkbxn7yupu
Oracle-efficient confidence envelopes for covariance functions in dense functional data
2016
Statistica sinica
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We consider nonparametric estimation of the covariance function for dense functional data using computationally efficient tensor product B-splines. ...
Simultaneous confidence envelopes are developed based on asymptotic theory to quantify the variability in the covariance estimator and to make global inferences on the true covariance. ...
We show the estimated covariance function and Using the simultaneous confidence envelopes, one can test other interesting hypotheses on the true covariance function, such as the true covariance being stationary ...
doi:10.5705/ss.2014-182
fatcat:abtnlwtjg5g3lbvp6azcvjuqna
Fast and Fair Simultaneous Confidence Bands for Functional Parameters
[article]
2022
arXiv
pre-print
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In this work, we present a new methodology for constructing simultaneous confidence bands for functional parameter estimates. ...
of the full covariance function and thus can be used in the case of fragmentary functional data. ...
We thank the mathematical research institute MATRIX in Creswick, Australia and the Simons Institute for the Theory of Computing at the UC Berkeley where parts of this research was performed. ...
arXiv:1910.00131v5
fatcat:zpwvmkq6uzbt3a5abocheoyfya
Confidence surfaces for the mean of locally stationary functional time series
[article]
2022
arXiv
pre-print
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The problem of constructing a simultaneous confidence band for the mean function of a locally stationary functional time series { X_i,n (t) }_i = 1, ..., n is challenging as these bands can not be built ...
On the other hand, for stationary functional data, simultaneous confidence bands can be built on classical central theorems for Banach space valued random variables and the limit distribution of the maximum ...
Acknowlegement Holger Dette gratefully acknowledges Collaborative Research Center "Statistical modeling of nonlinear dynamic processes" (SFB 823, Project A1, C1) of the German Research Foundation ...
arXiv:2109.03641v2
fatcat:3vzipxlhlreg5j4odkdzmtijbu
Smoothing and Mean–Covariance Estimation of Functional Data with a Bayesian Hierarchical Model
2016
Bayesian Analysis
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While many statistical tools have been developed for functional data analysis, the issue of smoothing all functional observations simultaneously is less studied. ...
and an Inverse-Wishart process prior for the covariance function. ...
Acknowledgments The authors would like to thank all colleagues in the PO1 project (supported by NIH grant PO1-CA-082710) for collecting the spectroscopy data and the Children's Nutrition Research ...
doi:10.1214/15-ba967
pmid:34457106
pmcid:PMC8387981
fatcat:pojdahmb2fbe3gyry65eojt4x4
Semiparametric Mixed Models for Medical Monitoring Data: An Overview
2015
Journal of Biometrics & Biostatistics
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It is well known that accounting for intra-and inter-subject variability is a pervasive issue in longitudinal data analysis. ...
It is often of interest to investigate differences between experimental groups in a study or identify the onset of rapid changes in the response of interest using medical monitoring data; however, analytic ...
Richard Charnigo, for their thoughtful comments, which have substantially improved the content of this paper. ...
doi:10.4172/2155-6180.1000234
pmid:29593934
pmcid:PMC5868984
fatcat:pbwpkowrsfdrhd76vdkbvldxsq
Functional Data Analysis for Sparse Longitudinal Data
2005
Journal of the American Statistical Association
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Asymptotic pointwise and simultaneous confidence bands are obtained for predicted individual trajectories, based on asymptotic distributions, for simultaneous bands under the assumption of a finite number ...
Functional data analysis for sparse longitudinal data enables prediction of individual smooth trajectories even if only one or few measurements are available for a subject. ...
We note that the trajectories obtained for the complete data are found to be enclosed in the simultaneous 95% confidence bands constructed from the sparse data. ...
doi:10.1198/016214504000001745
fatcat:uplgj4o2lzdzflctlmfmx5zeey
Statistical Analysis of Large Cross-Covariance and Cross-Correlation Matrices Produced by fMRI Images
2013
Journal of Biometrics & Biostatistics
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; (iii) develop the theory and methods of adaptive simultaneous confidence intervals and adaptive rate-minimax thresholding estimation for the matrices. ...
Furthermore, the matrices have an interesting property to have both sparse and dense rows and columns. ...
(b) Simultaneous (1-α) confidence interval for cross-covariances σ ij , i ∈{1,2,…,p 1 }, j ∈{1,2,…,p 2 } is n U n U α α ρ γ ρ γ − − − + where γ α is defined in (b). ...
doi:10.4172/2155-6180.1000193
fatcat:wrswjy6tv5cv7dhjmiwb4ram6y
Sparsely Observed Functional Time Series: Estimation and Prediction
[article]
2019
arXiv
pre-print
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Means of providing corresponding confidence bands are also investigated. ...
A simulation study interestingly suggests that sparse observation for a longer time period, may be provide better performance than dense observation for a shorter period, in the presence of smoothness. ...
confidence bands for the functional data of the said latent process (yellow). ...
arXiv:1811.06340v2
fatcat:sniecqajjna7pi7cr5t22s46q4
High resolution simulation of nonstationary Gaussian random fields
2016
Computational Statistics & Data Analysis
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Simulation of random fields is a fundamental requirement for many spatial analyses. For small spatial networks, simulations can be produced using direct manipulations of the covariance matrix. ...
The nonstationary covariance function is estimated nonparametrically, and the deformation function is then estimated in a variational framework. ...
Acknowledgements The author wishes to thank Michael Scheuerer for helpful discussions during the development of this work. ...
doi:10.1016/j.csda.2016.03.005
fatcat:bf5hboqudnfbtiufs72hznccp4
Sparsely observed functional time series: estimation and prediction
2020
Electronic Journal of Statistics
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Means of providing corresponding confidence bands are also investigated. ...
A simulation study interestingly suggests that sparse observation for a longer time period may provide better performance than dense observation for a shorter period, in the presence of smoothness. ...
Acknowledgements We wish to thank the editors and reviewers for their thoughtful and constructive comments. ...
doi:10.1214/20-ejs1690
fatcat:jbotp5djajg2fi7oggs54mf7o4
Interpolation of nonstationary high frequency spatial–temporal temperature data
2013
Annals of Applied Statistics
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We also describe methods for handling spatial-temporal jumps in the data to interpolate a slow-moving cold front. ...
The model is fit by maximizing an approximate likelihood, and the conditional simulations result in well-calibrated confidence intervals for the predicted temperatures. ...
As the month progresses, the simulated temperatures tend to drift away from the data, resulting in very wide confidence bands for most of the month. ...
doi:10.1214/13-aoas633
fatcat:o6p7r4yh2fhupa4dn6punixw74
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