Functional principal component analysis (FPCA) based on the Karhunen–Loève decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation, but also by the actual question of dynamics of...

We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependen...

The Gaia optical reference frame is intrinsically undefined with respect to global orientation and spin, so it needs be anchored in the radio-based International Celestial Reference Frame (ICRF) provide a referenced quasi-inertial celestial coordinate system. link between two fundamental frames realized through samples of distant extragalactic sources, mostly AGNs quasars, but only smaller samp...

Functional principal component analysis is essential in functional data analysis, but the inference will become unconvincing when non-Gaussian characteristics occur (e.g., heavy tail and skewness). The focus of this manuscript to develop a robust methodology deal with longitudinal data, where sparsity irregularity along non-negligible measurement errors must be considered. We introduce Kendall’...

Recent advances in computer recording and storing technology have tremendously increased the presence of functional data, whose graphical representation can be infinitedimensional curve, image, or shape. When the same functional object is observed over a period of time, such data are known as functional time series. This article makes first attempt to describe several techniques (centered aroun...

Over the last few years many methods have been developed for analyzing functional data with different objectives. The purpose of this paper is to predict a binary response variable in terms of a functional variable whose sample information is given by a set of curves measured without error. In order to solve this problem we formulate a functional logistic regression model and propose its estima...

Recent advances in computer recording and storing technology have tremendously increased the presence of functional data, whose graphical representation can be infinite-dimensional curve, image, or shape. When the same functional object is observed over a period of time, such data are known as functional time series. This article makes first attempt to describe several techniques (centered arou...

We present a nonparametric method to forecast a seasonal univariate time series, and propose four dynamic updating methods to improve point forecast accuracy. Our methods consider a seasonal univariate time series as a functional time series. We propose first to reduce the dimensionality by applying functional principal component analysis to the historical observations, and then to use univaria...

a procedure for an efficient recovering of reflectance spectra of acrylic paint samples from cie tristimulus color values is described. by fixing a certain criteria based on color difference value, the proposed technique preliminarily selects a series of suitable samples from a main dataset containing the reflectance values of a series of different acrylic paint samples, based on the color spec...