Related papers: Concerns with functional depth
The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth…
Functional depth is used for ranking functional observations from most outlying to most typical. The ranks produced by functional depth have been proposed as the basis for functional classifiers, rank tests, and data visualization…
A functional data depth provides a center-outward ordering criterion which allows the definition of measures such as median, trimmed means, central regions or ranks in a functional framework. A functional data depth can be global or local.…
We introduce a novel collection of uniqueness problems, with related sampling and interpolation issues. We call them deep zero problems, as they are concerned with local properties at a small number of given points.
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…
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…
The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…
We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projection directions, the proposed depth does not suffer from the…
In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities…
We examine problems due to lack of domain closure and definability preservation
We discuss some different results on Sidon-type inequalities and on the space of quasi-continuous functions.
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…
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…
We study a sharp fractional Moser-Trudinger type inequality in dimension 1, its compactness properties and the critical points of a functional associeted to the inequality.
The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths…