Name: Evaluating the complexity of some families of functional data
Keywords: Classificació AMS::60 Probability theory and stochastic processes::60G Stochastic processes, 330, complexity index, kNN estimation, Random processe, log-Volugram, :62 Statistics::62G Nonparametric inference [Classificació AMS], knn estimation, Small ball probability, log--Volugram

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2018Publisher:Universitat Rovira i VirgiliJournal:Sort-statistics and Operations Research Transactions, volume 42, pages 27-44

Authors: Bongiorno, Enea; Goia, Aldo; Vieu, Philippe;

doi: 10.2436/20.8080.02.67

handle: 20.500.11797/RP2471 , 2117/178501 , 11579/94463

Evaluating the complexity of some families of functional data

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Abstract

In this paper we study the complexity of a functional data set drawn from particular processes by means of a two-step approach. The first step considers a new graphical tool for assessing to which family the data belong: the main aim is to detect whether a sample comes from a monomial or an exponential family. This first tool is based on a nonparametric kNN estimation of small ball probability. Once the family is specified, the second step consists in evaluating the extent of complexity by estimating some specific indexes related to the assigned family. It turns out that the developed methodology is fully free from assumptions on model, distribution as well as dominating measure. Computational issues are carried out by means of simulations and finally the method is applied to analyse some financial real curves dataset.

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Keywords

Classificació AMS::60 Probability theory and stochastic processes::60G Stochastic processes, 330, complexity index, kNN estimation, Random processe, log-Volugram, :62 Statistics::62G Nonparametric inference [Classificació AMS], knn estimation, Small ball probability, log--Volugram, Complexity class, Small ball probability, log-Volugram, random processes, complexity class, complexity index, knn estimation, functional data analysis, Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica, Complexity index, Complexity cla, functional data analysis, Small Ball Probability, Random processes, :60 Probability theory and stochastic processes::60G Stochastic processes [Classificació AMS], Functional data analysis, Log-volugram, random processes, :Matemàtiques i estadística::Estadística matemàtica [Àrees temàtiques de la UPC], Functional Data Analysis, complexity class, Knn estimation, Classificació AMS::62 Statistics::62G Nonparametric inference, 62-09, 62G05, 60G99

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