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Open AccessArticle

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

by Honglong You 1,* and Yuan Gao 2
1
School of Statistics, Qufu Normal University, Qufu 273165, China
2
School of Mathematics, Qufu Normal University, Qufu 273165, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(6), 506; https://doi.org/10.3390/math7060506
Received: 15 April 2019 / Revised: 27 May 2019 / Accepted: 27 May 2019 / Published: 3 June 2019
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
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. View Full-Text
Keywords: Wiener–Poisson risk model; survival probability; Nonparametric threshold estimation Wiener–Poisson risk model; survival probability; Nonparametric threshold estimation
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You, H.; Gao, Y. Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model. Mathematics 2019, 7, 506.

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