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

Yu, Shan; Wang, Guannan; Wang, Li; Yang, Lijian

doi:10.5705/ss.202019.0188

Cited by 9 publications

(7 citation statements)

References 45 publications

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“…Remark 3. In Theorem 2, the condition n A n|∆| d+2 = o(1) is used for undersmoothing of the slope estimator, which is widely applied in the series approximating estimations (Yu et al, 2020(Yu et al, , 2021. By consistently estimating the asymptotic variance σ β (t, u), the result in Theorem 2 can be used to establish the pointwise confidence interval of the slope function.…”

Section: Theoretical Resultsmentioning

confidence: 99%

Simultaneous Functional Quantile Regression

Hu¹,

Hu²,

Liu³

et al. 2024

STAT SINICA

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The conventional method for functional quantile regression (FQR) is to fit the regression model for each quantile of interest separately. Therefore, the slope function of the regression, as a bivariate function of time and quantile, is estimated as a univariate function of time for each fixed quantile. There are several limitations to this conventional strategy. For example, the monotonicity of conditional quantiles can not be guaranteed, and the smoothness of the slope estimator as a bivariate function can not be controlled. In this paper, we develop a new framework for functional quantile regression. We propose to simultaneously fit the functional quantile regression model for multiple quantiles with the help of a bivariate basis under some constraints so that the estimated quantiles satisfy the monotonicity conditions. Meanwhile, the smoothness of the slope estimator is controlled.The proposed estimator for the slope function is shown to be asymptotically consistent. In addition, we also establish its asymptotic normality. Simulation studies are implemented to evaluate the finite sample performance of the proposed method in comparison with the

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Section: Theoretical Resultsmentioning

confidence: 99%

Simultaneous Functional Quantile Regression

Hu¹,

Hu²,

Liu³

et al. 2024

STAT SINICA

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“…, N i , which forms an M -row array with N i points in the i-th row, see Figure 14(a) and Figure 18(a). The similar data setting was also considered in Yu et al (2021).…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference for Mean Function of Longitudinal Imaging Data over Complicated Domains

Hu¹,

Li²

2024

STAT SINICA

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Motivated by longitudinal imaging data possessing inherent spatial and temporal correlation, we propose a novel procedure to estimate its mean function. Functional moving average is applied to depict the dependence among temporally ordered images and flexible bivariate splines over triangulations are utilized to handle the irregular domain of images which is common in imaging studies. Both global and local asymptotic properties of the bivariate spline estimator for mean function are established with simultaneous confidence corridors (SCCs) as a theoretical byproduct. Under some mild conditions, the proposed estimator and its accompanying SCCs are shown to be consistent and oracle efficient as if all images were entirely observed without errors. The finite sample performance of the proposed method through Monte Carlo simulation experiments strongly corroborates the asymptotic theory. The proposed method is further illustrated by analyzing two sea water potential temperature data sets.

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“…We then define a direct model for the estimation of a functional discriminant direction in the parametrizing space exploiting a convenient reformulation of the problem into a regularized functional linear regression model, where appropriate differential spatial regularization is introduced to produce interpretable and well-defined estimates. While several regularized regression models for functional data supported on multidimensional domains have been proposed (Goldsmith, Huang, and Crainiceanu 2014;Wang and Zhu 2017;Kang, Reich, and Staicu 2018;Feng et al 2020;Yu et al 2021), these are limited to flat domains as they rely on a global Cartesian coordinate system, which is in general not available on non-linear domains. Moreover, some of these approaches rely on pre-computations of the covariance structure of the functional predictors, which is ultimately not possible in our final application due to the high dimensionality of the data.…”

Section: Introductionmentioning

confidence: 99%

Interpretable discriminant analysis for functional data supported on random non-linear domains

Lila¹,

Zhang²,

Rane³

2021

Preprint

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We introduce a novel framework for the classification of functional data supported on non-linear, and possibly random, manifold domains. The motivating application is the identification of subjects with Alzheimer's disease from their cortical surface geometry and associated cortical thickness map. The proposed model is based upon a reformulation of the classification problem into a regularized multivariate functional linear regression model. This allows us to adopt a direct approach to the estimation of the most discriminant direction while controlling for its complexity with appropriate differential regularization. Our approach does not require prior estimation of the covariance structure of the functional predictors, which is computationally not feasible in our application setting. We provide a theoretical analysis of the out-of-sample prediction error of the proposed model and explore the finite sample performance in a simulation setting. We apply the proposed method to a pooled dataset from the Alzheimer's Disease Neuroimaging Initiative and the Parkinson's Progression Markers Initiative, and are able to estimate discriminant directions that capture both cortical geometric and thickness predictive features of Alzheimer's Disease, which are consistent with the existing neuroscience literature.

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

Cited by 9 publications

References 45 publications

Simultaneous Functional Quantile Regression

Simultaneous Functional Quantile Regression

Statistical Inference for Mean Function of Longitudinal Imaging Data over Complicated Domains

Interpretable discriminant analysis for functional data supported on random non-linear domains

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