Asymptotic Behaviour of Discretised Functionals of Long-Range Dependent Functional Data

05/24/2019
by   Tareq Alodat, et al.
0

The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given by these functionals. It is shown that in the discrete sampling case additive functionals have the same asymptotic distribution as the corresponding integral functionals for the continuous functional data case. These results are applied to obtain non-central limit theorems for weighted additive functionals of random fields. As the majority of known results concern the discrete sampling case the developed methodology helps in translating these results to functional data without deriving them again. Numerical studies suggest that the theoretical findings are valid for wider classes of long-range dependent data.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/22/2019

On LSE in regression model for long-range dependent random fields on spheres

We study the asymptotic behaviour of least squares estimators in regress...
research
12/18/2018

Limit theorems for filtered long-range dependent random fields

This article investigates general scaling settings and limit distributio...
research
05/01/2020

Reduction principle for functionals of strong-weak dependent vector random fields

We prove the reduction principle for asymptotics of functionals of vecto...
research
10/19/2018

Non-central limit theorems for functionals of random fields on hypersurfaces

This paper derives non-central asymptotic results for non-linear integra...
research
11/16/2019

Inference in Models of Discrete Choice with Social Interactions Using Network Data

This paper studies inference in models of discrete choice with social in...
research
05/27/2019

Ordinal Patterns in Long-Range Dependent Time Series

We analyze the ordinal structure of long-range dependent time series. To...
research
03/05/2020

Central limit theorems for additive functionals and fringe trees in tries

We give general theorems on asymptotic normality for additive functional...

Please sign up or login with your details

Forgot password? Click here to reset