ﻻ يوجد ملخص باللغة العربية
A data depth measures the centrality of a point with respect to an empirical distribution. Postulates are formulated, which a depth for functional data should satisfy, and a general approach is proposed to construct multivariate data depths in Banach spaces. The new approach, mentioned as Phi-depth, is based on depth infima over a proper set Phi of R^d-valued linear functions. Several desirable properties are established for the Phi-depth and a generalized version of it. The general notions include many new depths as special cases. In particular a location-slope depth and a principal component depth are introduced.
The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, a majority of the reconstruction methods rely on estimating the covariance matrix or the components of its eigendeco
Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a point and a
Smart metering infrastructures collect data almost continuously in the form of fine-grained long time series. These massive time series often have common daily patterns that are repeated between similar days or seasons and shared between grouped mete
We develop a novel exploratory tool for non-Euclidean object data based on data depth, extending the celebrated Tukeys depth for Euclidean data. The proposed metric halfspace depth, applicable to data objects in a general metric space, assigns to dat
A novel approach to perform unsupervised sequential learning for functional data is proposed. Our goal is to extract reference shapes (referred to as templates) from noisy, deformed and censored realizations of curves and images. Our model generalize