The law of iterated logarithm for the estimations of diffusion-type processes

Abstract This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexity argument, it is proved that the estimator for different values of γ satisfies th...

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Main Authors:	Mingzhi Mao, Gang Huang
Format:	Article
Language:	English
Published:	SpringerOpen 2020-01-01
Series:	Advances in Difference Equations
Subjects:	The law of iterated logarithm Diffusion-type processes Approach of argmins Objective function
Online Access:	https://doi.org/10.1186/s13662-020-2506-5

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spelling	doaj-8ec3914e3d934f6ab933dfb94ca1fa032021-01-17T12:52:09ZengSpringerOpenAdvances in Difference Equations1687-18472020-01-012020111510.1186/s13662-020-2506-5The law of iterated logarithm for the estimations of diffusion-type processesMingzhi Mao0Gang Huang1School of Mathematics and Physics, China University of GeosciencesSchool of Mathematics and Physics, China University of GeosciencesAbstract This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexity argument, it is proved that the estimator for different values of γ satisfies the iterated logarithm law. The result also presents the exponential convergence principle for the estimator converging to the true value.https://doi.org/10.1186/s13662-020-2506-5The law of iterated logarithmDiffusion-type processesApproach of argminsObjective function
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mingzhi Mao Gang Huang
spellingShingle	Mingzhi Mao Gang Huang The law of iterated logarithm for the estimations of diffusion-type processes Advances in Difference Equations The law of iterated logarithm Diffusion-type processes Approach of argmins Objective function
author_facet	Mingzhi Mao Gang Huang
author_sort	Mingzhi Mao
title	The law of iterated logarithm for the estimations of diffusion-type processes
title_short	The law of iterated logarithm for the estimations of diffusion-type processes
title_full	The law of iterated logarithm for the estimations of diffusion-type processes
title_fullStr	The law of iterated logarithm for the estimations of diffusion-type processes
title_full_unstemmed	The law of iterated logarithm for the estimations of diffusion-type processes
title_sort	law of iterated logarithm for the estimations of diffusion-type processes
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2020-01-01
description	Abstract This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexity argument, it is proved that the estimator for different values of γ satisfies the iterated logarithm law. The result also presents the exponential convergence principle for the estimator converging to the true value.
topic	The law of iterated logarithm Diffusion-type processes Approach of argmins Objective function
url	https://doi.org/10.1186/s13662-020-2506-5
work_keys_str_mv	AT mingzhimao thelawofiteratedlogarithmfortheestimationsofdiffusiontypeprocesses AT ganghuang thelawofiteratedlogarithmfortheestimationsofdiffusiontypeprocesses AT mingzhimao lawofiteratedlogarithmfortheestimationsofdiffusiontypeprocesses AT ganghuang lawofiteratedlogarithmfortheestimationsofdiffusiontypeprocesses
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The law of iterated logarithm for the estimations of diffusion-type processes

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