Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model

Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model

In this paper, we consider the Wiener−Poisson risk model, which consists of a Wiener process and a compound Poisson process. Given the discrete record of observations, we use a threshold method and a regularized Laplace inversion technique to estimate the survival probability. In addition,...

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Bibliographic Details
Main Authors: Honglong You, Yuan Gao
Format: Article
Language:English
Published: MDPI AG 2019-06-01
Series:Mathematics
Subjects:
Wiener–Poisson risk model
survival probability
Nonparametric threshold estimation
Online Access:https://www.mdpi.com/2227-7390/7/6/506
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spelling doaj-38170a42c98546ae905f571f54749d832020-11-24T21:33:23ZengMDPI AGMathematics2227-73902019-06-017650610.3390/math7060506math7060506Non-Parametric Threshold Estimation for the Wiener–Poisson Risk ModelHonglong You0Yuan Gao1School of Statistics, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematics, Qufu Normal University, Qufu 273165, ChinaIn this paper, we consider the Wiener−Poisson risk model, which consists of a Wiener process and a compound Poisson process. Given the discrete record of observations, we use a threshold method and a regularized Laplace inversion technique to estimate the survival probability. In addition, we also construct an estimator for the distribution function of jump size and study its consistency and asymptotic normality. Finally, we give some simulations to verify our results.https://www.mdpi.com/2227-7390/7/6/506Wiener–Poisson risk modelsurvival probabilityNonparametric threshold estimation
collection DOAJ
language English
format Article
sources DOAJ
author Honglong You
Yuan Gao
spellingShingle Honglong You
Yuan Gao
Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model
Mathematics
Wiener–Poisson risk model
survival probability
Nonparametric threshold estimation
author_facet Honglong You
Yuan Gao
author_sort Honglong You
title Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model
title_short Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model
title_full Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model
title_fullStr Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model
title_full_unstemmed Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model
title_sort non-parametric threshold estimation for the wiener–poisson risk model
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-06-01
description In this paper, we consider the Wiener−Poisson risk model, which consists of a Wiener process and a compound Poisson process. Given the discrete record of observations, we use a threshold method and a regularized Laplace inversion technique to estimate the survival probability. In addition, we also construct an estimator for the distribution function of jump size and study its consistency and asymptotic normality. Finally, we give some simulations to verify our results.
topic Wiener–Poisson risk model
survival probability
Nonparametric threshold estimation
url https://www.mdpi.com/2227-7390/7/6/506
work_keys_str_mv AT honglongyou nonparametricthresholdestimationforthewienerpoissonriskmodel
AT yuangao nonparametricthresholdestimationforthewienerpoissonriskmodel
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