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Simultaneous Confidence Band for Stationary Covariance Function of Dense Functional Data [article]

Jiangyan Wang, Guanqun Cao, Li Wang, Lijian Yang
2019 arXiv   pre-print
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

Jingjing Yang, Peng Ren
2019 Journal of Statistical Software  
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]

Jingjing Yang, Peng Ren
2017 arXiv   pre-print
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

Guanqun Cao, Lily Wang, Yehua Li, Lijian Yang
2017 Statistica sinica  
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

Guanqun Cao, Li Wang, Yehua Li, Lijian Yang
2016 Statistica sinica  
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]

Dominik Liebl, Matthew Reimherr
2022 arXiv   pre-print
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]

Holger Dette, Weichi Wu
2022 arXiv   pre-print
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

Jingjing Yang, Hongxiao Zhu, Taeryon Choi, Dennis D. Cox
2016 Bayesian Analysis  
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

Szczesniak RD Dan Li
2015 Journal of Biometrics & Biostatistics  
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

Fang Yao, Hans-Georg Müller, Jane-Ling Wang
2005 Journal of the American Statistical Association  
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

Ekaterina Smirnova
2013 Journal of Biometrics & Biostatistics  
; (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]

Tomáš Rubín, Victor M. Panaretos
2019 arXiv   pre-print
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

William Kleiber
2016 Computational Statistics & Data Analysis  
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

Tomáš Rubín, Victor M. Panaretos
2020 Electronic Journal of Statistics  
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

Joseph Guinness, Michael L. Stein
2013 Annals of Applied Statistics  
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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