Weak convergences of marked empirical processes with applications to goodness-of-fit tests for Markovian processes

08/17/2018
by   Koji Tsukuda, et al.
0

In this paper, weak convergences of marked empirical processes in L^2(R,ν) and their applications to statistical goodness-of-fit tests are provided, where L^2(R,ν) is a set of equivalence classes of the square integrable functions on R with respect to a finite Borel measure ν. The results obtained in our framework of weak convergences are, in the topological sense, weaker than those in the Skorokhod topology on a space of cádlág functions or the uniform topology on a space of bounded functions, which have been well studied in previous works. However, our results have the following merits: (1) avoiding a smoothness condition which sometimes does not hold for some time series models appearing in statistics; (2) treating a weight function which make us possible to propose an Anderson--Darling type test statistics for goodness-of-fit tests. Indeed, the applications presented in this paper are novel.

READ FULL TEXT
research
10/16/2019

Asymptotic Theory of L-Statistics and Integrable Empirical Processes

This paper develops asymptotic theory of integrals of empirical quantile...
research
03/01/2020

Smooths Tests of Goodness-of-fit for the Newcomb-Benford distribution

The Newcomb-Benford probability distribution is becoming very popular in...
research
08/30/2018

Tests de bondad de ajuste para la distribución Poisson bivariante

The objective of this text is to propose and study goodness-of-fit tests...
research
01/13/2019

Asymptotics of an empirical bridge of a regression on induced order statistics

We propose a class of tests for linear regression on concomitants (induc...
research
03/11/2018

Empirical bounds for functions with weak interactions

We provide sharp empirical estimates of expectation, variance and normal...
research
10/25/2022

Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions

This paper adopts a tool from computational topology, the Euler characte...
research
01/24/2019

Raking-ratio empirical process with auxiliary information learning

The raking-ratio method is a statistical and computational method which ...

Please sign up or login with your details

Forgot password? Click here to reset