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

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

A review of Tourism Supply Chain based on the Perspective of Sustainable Development

In this paper, the theory of traditional manufacturing supply chain management is applied to the study of tourism supply chain. Based on the view of sustainable development, a large-scale relevant literature review concerning tourism supply chain and sustainable supply chain is performed, in which current situation and deficiency are reviewed. In order to solve the problem, this paper tries to discuss and establish a new sustainable supply chain pattern, in which tourist attractions are taken as core enterprises. Furthermore, this paper tries to find an optimization strategy to do facilitate long-term sustainable development of tourism and improve the tourism industry profitability and competitiveness Keywords: tourism supply chain， sustainable development， core enterpris

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

Confined Multilamellae Prefer Cylindrical Morphology

By evaporating a drop of lipid dispersion we generate the myelin morphology often seen in dissolving surfactant powders. We explain these puzzling nonequilibrium structures using a geometric argument: The bilayer repeat spacing increases and thus the repulsion between bilayers decreases when a multilamellar disk is converted into a myelin without gain or loss of material and with number of bilayers unchanged. Sufficient reduction in bilayer repulsion can compensate for the cost in curvature energy, leading to a net stability of the myelin structure. A numerical estimate predicts the degree of dehydration required to favor myelin structures over flat lamellae.Comment: 6 pages, 3 figures, submitted to Euro. Phys. J.