Covariate adjusted functional principal components analysis for longitudinal data

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal of this paper to develop two methods that do. In the first approach, both the mean and covariance functions depend on the covariate $Z$ and time scale $t$ while in the second approach only the mean function depends on the covariate $Z$. Both new approaches accommodate additional measurement errors and functional data sampled at regular time grids as well as sparse longitudinal data sampled at irregular time grids. The first approach to fully adjust both the mean and covariance functions adapts more to the data but is computationally more intensive than the approach to adjust the covariate effects on the mean function only. We develop general asymptotic theory for both approaches and compare their performance numerically through simulation studies and a data set.Comment: Published in at http://dx.doi.org/10.1214/09-AOS742 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Functional single index models for longitudinal data

A new single-index model that reflects the time-dynamic effects of the single index is proposed for longitudinal and functional response data, possibly measured with errors, for both longitudinal and time-invariant covariates. With appropriate initial estimates of the parametric index, the proposed estimator is shown to be $\sqrt{n}$-consistent and asymptotically normally distributed. We also address the nonparametric estimation of regression functions and provide estimates with optimal convergence rates. One advantage of the new approach is that the same bandwidth is used to estimate both the nonparametric mean function and the parameter in the index. The finite-sample performance for the proposed procedure is studied numerically.Comment: Published in at http://dx.doi.org/10.1214/10-AOS845 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inverse regression for longitudinal data

Sliced inverse regression (Duan and Li [Ann. Statist. 19 (1991) 505-530], Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferr\'{e} and Yao [Statistics 37 (2003) 475-488, Statist. Sinica 15 (2005) 665-683] and Hsing and Ren [Ann. Statist. 37 (2009) 726-755] to functional covariates where the whole trajectories of random functional covariates are completely observed. The focus of this paper is to develop sliced inverse regression for intermittently and sparsely measured longitudinal covariates. We develop asymptotic theory for the new procedure and show, under some regularity conditions, that the estimated directions attain the optimal rate of convergence. Simulation studies and data analysis are also provided to demonstrate the performance of our method.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1193 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). With Correction

Smoothing dynamic positron emission tomography time courses using functional principal components

A functional smoothing approach to the analysis of PET time course data is presented. By borrowing information across space and accounting for this pooling through the use of a nonparametric covariate adjustment, it is possible to smooth the PET time course data thus reducing the noise. A new model for functional data analysis, the Multiplicative Nonparametric Random Effects Model, is introduced to more accurately account for the variation in the data. A locally adaptive bandwidth choice helps to determine the correct amount of smoothing at each time point. This preprocessing step to smooth the data then allows Subsequent analysis by methods Such as Spectral Analysis to be substantially improved in terms of their mean squared error

Innovating corporate share listing frameworks: a comparative study of SPAC regulatory regimes in the United Kingdom, Singapore, and Hong Kong

In the 2020s, special purpose acquisition companies (SPACs) have swiftly emerged as an alternative vehicle for global corporations that seek a public listing. This article aims to critically analyse the regulatory frameworks governing SPAC listings in three prominent common law jurisdictions: the United Kingdom, Singapore, and Hong Kong. It evaluates the latest corporate share listing reforms from a comparative perspective, shedding light on how each jurisdiction adapts to the dynamic nature of SPACs and addresses rising challenges regarding investor protection under their new listing regimes. The discussion focuses on the influence of international best practices and the cooperation among global regulatory authorities. By providing an in-depth comparative analysis of SPAC listing rules in London, Singapore, and Hong Kong, this article offers valuable insights for researchers, legal practitioners, policymakers, public companies, and their investors who seek to understand the regulatory landscape for SPACs and innovative corporate regimes in leading financial centres. The findings enhance our understanding of the strengths and weaknesses of the SPAC regulatory frameworks in each of the three jurisdictions, thus assisting stakeholders in making informed decisions in the rapidly evolving global financial landscape

A Functional Approach to Deconvolve Dynamic Neuroimaging Data.

Positron emission tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first-order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. To provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire three-dimensional volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both one-dimensional functions and 2D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.The research of Ci-Ren Jiang is supported in part by NSC 101-2118-M-001-013-MY2 (Taiwan); the research of Jane-Ling Wang is supported by NSF grants, DMS-09-06813 and DMS-12-28369. JA is supported by EPSRC grant EP/K021672/2. The authors would like to thank SAMSI and the NDA programme where some of this research was carried out.This is the final version of the article. It first appeared from Taylor & Francis via http://dx.doi.org/10.1080/01621459.2015.106024