Functional envelope for model-free sufficient dimension reduction

Zhang, Xin; Wang, Chong; Wu, Yichao

doi:10.1016/j.jmva.2017.09.010

Cited by 14 publications

(7 citation statements)

References 51 publications

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“…First, using multivariate outcome functional data models (Kang et al, 2014;Cao et al, 2019) to incorporate auxiliary information such as demographic information will help improve the clustering and disease prediction accuracy (Xue et al, 2018). It will also be of interest to perform other functional data dimension reduction methods (Zhang et al, 2018) instead of FPCA to extract useful information for clustering purpose. In addition, proposing an efficient sampling algorithm without tuning parameter selection and considering a nonstationary spatial structure are both important future directions.…”

Section: Discussionmentioning

confidence: 99%

Spatial homogeneity learning for spatially correlated functional data with application to COVID-19 Growth rate curves

Pan¹,

Shen²,

Guo³

2020

Preprint

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We study the spatial heterogeneity effect on regional COVID-19 pandemic timing and severity by analyzing the COVID-19 growth rate curves in the United States. We propose a geographically detailed functional data grouping method equipped with a functional conditional autoregressive (CAR) prior to fully capture the spatial correlation in the pandemic curves. The spatial homogeneity pattern can then be detected by a geographically weighted Chinese restaurant process prior which allows both locally spatially contiguous groups and globally discontiguous groups. We design an efficient Markov chain Monte Carlo (MCMC) algorithm to simultaneously infer the posterior distributions of the number of groups and the grouping configuration of spatial functional data. The superior numerical performance of the proposed method over competing methods is demonstrated using simulated studies and an application to COVID-19 state-level and county-level data study in the United States.

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Section: Discussionmentioning

confidence: 99%

Spatial homogeneity learning for spatially correlated functional data with application to COVID-19 Growth rate curves

Pan¹,

Shen²,

Guo³

2020

Preprint

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“…There exist some recent likelihood-based methods (Bura & Forzani, 2015;Bura et al, 2016) which are not covered here for brevity. Envelope model, proposed in (Cook et al, 2010) and improved in (Zhang et al, 2018;Zhang & Chen, 2020), is also another likelihood-based method not covered here.…”

Section: Likelihood-based Methodsmentioning

confidence: 99%

Sufficient Dimension Reduction for High-Dimensional Regression and Low-Dimensional Embedding: Tutorial and Survey

Ghojogh¹,

Ghodsi²,

Karray³

et al. 2021

Preprint

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“…Let 0 < u ≤ r denotes the structural dimension of the envelope, where u can be selected using a modified information criterion such as modified BIC (Li and Zhang (2017)), model free dimension selection such as full Grassmanian (FG; Zhang and Mai, 2017) and the 1-D algorithm (Cook and Zhang, 2016) , or crossvalidation. More details can be found in (Zhang and Mai, 2017;Zhang, Wang, and Wu, 2018) and the references therein.…”

Section: New Spatial Envelopementioning

confidence: 99%

New Parsimonious Multivariate Spatial Model: Spatial Envelope

Rekabdarkolaee¹,

Wang²,

Naji³

et al. 2020

STAT SINICA

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Dimension reduction provides a useful tool for analyzing high dimensional data. The recently developed Envelope method is a parsimonious version of the classical multivariate regression model through identifying a minimal reducing subspace of the responses. However, existing envelope methods assume an independent error structure in the model. While the assumption of independence is convenient, it does not address the additional complications associated with spatial or temporal correlations in the data. In this article, we introduce a Spatial Envelope method for dimension reduction in the presence of dependencies across space. We study the asymptotic properties of the proposed estimators and show that the asymptotic variance of the estimated regression coefficients under the spatial envelope model is smaller than that from the traditional maximum likelihood estimation. Furthermore, we present a computationally efficient approach for inference. The efficacy of the new approach is investigated through simulation studies and an analysis of an Air Quality Standard (AQS) dataset from the Environmental Protection Agency (EPA).

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Functional envelope for model-free sufficient dimension reduction

Cited by 14 publications

References 51 publications

Spatial homogeneity learning for spatially correlated functional data with application to COVID-19 Growth rate curves

Spatial homogeneity learning for spatially correlated functional data with application to COVID-19 Growth rate curves

Sufficient Dimension Reduction for High-Dimensional Regression and Low-Dimensional Embedding: Tutorial and Survey

New Parsimonious Multivariate Spatial Model: Spatial Envelope

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