A simultaneous confidence corridor for varying coefficient regression with sparse functional data

Gu, Lei; Wang, Li; Härdle, Wolfgang Karl; Yang, Lijian

doi:10.1007/s11749-014-0392-4

Cited by 34 publications

(17 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Gu et al . () and Chang et al . () proposed the SCC for coefficient functions in the function‐on‐scalar regression model.…”

Section: Introductionmentioning

confidence: 88%

Simultaneous confidence corridors for mean functions in functional data analysis of imaging data

Wang

et al. 2019

Biometrics

Self Cite

View full text Add to dashboard Cite

Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over triangulations to handle an irregular domain of the images that is common in brain imaging studies and in other biomedical imaging applications. The proposed spline estimators of the mean functions are shown to be consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. The procedure is also extended to the two‐sample case in which we focus on comparing the mean functions from two populations of imaging data. Through Monte Carlo simulation studies, we examine the finite sample performance of the proposed method. Finally, the proposed method is applied to analyze brain positron emission tomography data in two different studies. One data set used in preparation of this article was obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

show abstract

“…Gu et al . () and Chang et al . () proposed the SCC for coefficient functions in the function‐on‐scalar regression model.…”

Section: Introductionmentioning

confidence: 88%

Simultaneous confidence corridors for mean functions in functional data analysis of imaging data

Wang

et al. 2019

Biometrics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Assumptions (A1) and (A2) are similar to Assumptions (A1) and (A2) in Gu et al (2014) and Assumptions (A1)-(A3) in Huang et al (2004). Assumption (A3) is analogous to Assumption (A5) in Gu et al (2014), ensuring that X i is not multicollinear. Assumption (A5) requires that be of similar size, and suggests the use of more uniform triangulations with smaller shape parameters.…”

Section: Asymptotic Properties Of the Bpst Estimatorsmentioning

confidence: 91%

Multivariate Spline Estimation and Inference for Image-on-Scalar Regression

Yu¹,

Wang²,

Wang

et al. 2021

STAT SINICA

Self Cite

View full text Add to dashboard Cite

Motivated by recent work of analyzing data in the biomedical imaging studies, we consider a class of image-on-scalar regression models for imaging responses and scalar predictors. We propose to use flexible multivariate splines over triangulations to handle the irregular domain of the objects of interest on the images and other characteristics of images. The proposed estimators of the coefficient functions are proved to be root-n consistent and asymptotically normal under some regularity conditions. We also provide a consistent and computationally efficient estimator of the covariance function. Asymptotic pointwise confidence intervals (PCIs) and data-driven simultaneous confidence corridors (SCCs) for the coefficient functions are constructed. Our method can simultaneously estimate and make inferences of the coefficient functions while incorporating the spatial heterogeneity and spatial correlation. A highly efficient and scalable estimation algorithm is developed. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed method. The proposed method is applied to the spatially normalized Positron Emission Tomography (PET) data of Alzheimer's Disease Neuroimaging Initiative (ADNI).

show abstract

“…For instance, Ma, Yang and Carroll [20] constructed SCBs for the mean functions via piece-wise constant spline fitting. Gu et al [12] constructed piece-wise constant SCBs for B-spline nonparametric regression of sparse longitudinal data. As pointed out in [34], the piece-wise constant spline method suffers from consisting of discontinuous step functions.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous nonparametric regression analysis of sparse longitudinal data

Cao¹,

Liu²,

Zhou³

2018

Bernoulli

View full text Add to dashboard Cite

Longitudinal data arise frequently in many scientific inquiries. To capture the dynamic relationship between longitudinal covariates and response, varying coefficient models have been proposed with point-wise inference procedures. This paper considers the challenging problem of asymptotically accurate simultaneous inference of varying coefficient models for sparse and irregularly observed longitudinal data via the local linear kernel method. The error and covariate processes are modeled as very general classes of non-Gaussian and non-stationary processes and are allowed to be statistically dependent. Simultaneous confidence bands (SCBs) with asymptotically correct coverage probabilities are constructed to assess the overall pattern and magnitude of the dynamic association between the response and covariates. A simulation based method is proposed to overcome the problem of slow convergence of the asymptotic results. Simulation studies demonstrate that the proposed inference procedure performs well in realistic settings and is favored over the existing point-wise and Bonferroni methods. A longitudinal dataset from the Chicago Health and Aging Project is used to illustrate our methodology.

show abstract

A simultaneous confidence corridor for varying coefficient regression with sparse functional data

Abstract: We consider a varying coefficient regression model for sparse functional data, with time varying response variable depending linearly on some time independent covariates with co-

Cited by 34 publications

References 35 publications

Simultaneous confidence corridors for mean functions in functional data analysis of imaging data

Simultaneous confidence corridors for mean functions in functional data analysis of imaging data

Multivariate Spline Estimation and Inference for Image-on-Scalar Regression

Simultaneous nonparametric regression analysis of sparse longitudinal data

Contact Info

Product

Resources

About