The Sleep Heart Health Study (SHHS) is a comprehensive landmark study of sleep and its impacts on health outcomes. A primary metric of the SHHS is the in-home polysomnogram, which includes two electroencephalographic (EEG) channels for each subject, at two visits. The volume and importance of this data presents enormous challenges for analysis. To address these challenges, we introduce multilev...

Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively used in practical situations. In this work we focus on local covariance operators. They provide some pieces of information about the distribution of X around ...

Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure o...

We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex optimization problem through a novel Deflated Fantope Localization method and is implemented through an efficient algorithm to obtain the global optimum. We prove ...

Functional principal component analysis (FPCA) is a popular approach in functional data analysis to explore major sources of variation in a sample of random curves. These major sources of variation are represented by functional principal components (FPCs). Most existing FPCA approaches use a set of flexible basis functions such as B-spline basis to represent the FPCs, and control the smoothness...

Functional principal component analysis (FPCA) has played an important role in the development of functional time series analysis. This note investigates how FPCA can be used to analyze cointegrated and proposes a modification as novel statistical tool. Our modified not only provides asymptotically more efficient estimator cointegrating vectors, but also leads FPCA-based tests for examining ess...

the species of dioscorea (yam) are regarded as a staple food crop for millions of people in the tropical and subtropical regions of the world. it is regarded as an important food crop next to cereals and grains due to high yield storage of carbohydrates. economically, only few species are recognized for cultivation from agricultural point of view, in spite of its large species diversity. the sp...