Asymptotic normality of the minimum distance estimators for a Poisson process with a discontinuous intensity function

2001 ◽  
Vol 99 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Christophe Aubry ◽  
Ali Souleyman Dabye
Keyword(s):  
Asymptotic Normality ◽  
Poisson Process ◽  
Minimum Distance ◽  
Intensity Function ◽  
Minimum Distance Estimators

scholarly journals The Numerical Simulation for Asymptotic Normality of the Intensity Obtained as a Product of a Periodic Function with the Power Trend Function of a Nonhomogeneous Poisson Process

2020 ◽  
Vol 3 (3) ◽  
pp. 271-278
Author(s):  
Ikhsan Maulidi ◽  
Mahyus Ihsan ◽  
Vina Apriliani
Keyword(s):  
Numerical Simulation ◽  
Periodic Function ◽  
Asymptotic Normality ◽  
Poisson Process ◽  
Power Function ◽  
Observation Interval ◽  
Intensity Function ◽  
Nonhomogeneous Poisson Process ◽  
Trend Function ◽  
Kernel Type

In this article, we provided a numerical simulation for asymptotic normality of a kernel type estimator for the intensity obtained as a product of a periodic function with the power trend function of a nonhomogeneous Poisson Process. The aim of this simulation is to observe how convergence the variance and bias of the estimator. The simulation shows that the larger the value of power function in intensity function, it is required the length of the observation interval to obtain the convergent of the estimator.

Weak limit results for the extremes of a class of shot noise processes

1995 ◽  
Vol 32 (03) ◽  
pp. 707-726 ◽  
Author(s):  
Patrick Homble ◽  
William P. McCormick
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Impulse Response Function ◽  
Weak Limit ◽  
Intensity Function ◽  
Important Class ◽  
Homogeneous Poisson Process ◽  
Periodic Intensity ◽  
Non Homogeneous Poisson Process ◽  
Over Time

Shot noise processes form an important class of stochastic processes modeling phenomena which occur as shocks to a system and with effects that diminish over time. In this paper we present extreme value results for two cases — a homogeneous Poisson process of shocks and a non-homogeneous Poisson process with periodic intensity function. Shocks occur with a random amplitude having either a gamma or Weibull density and dissipate via a compactly supported impulse response function. This work continues work of Hsing and Teugels (1989) and Doney and O'Brien (1991) to the case of random amplitudes.

scholarly journals Fitting the Errors-in-variables Model Using High-order Cumulants and Moments

2017 ◽  
Vol 17 (1) ◽  
pp. 116-129 ◽  
Author(s):  
Timothy Erickson ◽  
Robert Parham ◽  
Toni M. Whited
Keyword(s):  
Method Of Moments ◽  
Minimum Distance ◽  
Generalized Method Of Moments ◽  
High Order ◽  
Moment Condition ◽  
Errors In Variables ◽  
Moment Estimation ◽  
Internal Support ◽  
Minimum Distance Estimators ◽  
High Order Cumulants

In this article, we consider a multiple mismeasured regressor errors-in-variables model. We present xtewreg, a command for using two-step generalized method of moments and minimum distance estimators that exploit overidentifying information contained in high-order cumulants or moments of the data. The command supports cumulant or moment estimation, internal support for the bootstrap with moment condition recentering, an arbitrary number of mismeasured regressors and perfectly measured regressors, and cumulants or moments up to an arbitrary degree. We also demonstrate how to use the estimators in the context of a corporate leverage regression.

Misspecified change-point estimation problem for a Poisson process

2001 ◽  
Vol 38 (A) ◽  
pp. 122-130 ◽  
Author(s):  
Ali S. Dabye ◽  
Yury A. Kutoyants
Keyword(s):  
Maximum Likelihood ◽  
Poisson Process ◽  
Change Point ◽  
Maximum Likelihood Estimate ◽  
Intensity Function ◽  
Point Estimation ◽  
Lower Function ◽  
Inhomogeneous Poisson Process ◽  
Change Point Estimation ◽  
Unknown Point

Consider an inhomogeneous Poisson process X on [0, T] whose unknown intensity function ‘switches' from a lower function g∗ to an upper function h∗ at some unknown point θ∗. What is known are continuous bounding functions g and h such that g∗(t) ≤ g(t) ≤ h(t) ≤ h∗(t) for 0 ≤ t ≤ T. It is shown that on the basis of n observations of the process X the maximum likelihood estimate of θ∗ is consistent for n →∞, and also that converges in law and in pth moment to limits described in terms of the unknown functions g∗ and h∗.

A linear random growth model

1990 ◽  
Vol 27 (3) ◽  
pp. 499-509 ◽  
Author(s):  
M. P. Quine ◽  
J. Robinson
Keyword(s):  
Asymptotic Normality ◽  
Poisson Process ◽  
Growth Model ◽  
Unit Interval ◽  
Asymptotic Expressions ◽  
Random Growth ◽  
Precise Asymptotic

Points start to form on an ‘uncovered' unit interval according to a Poisson process with parameter λ. From newly formed points a covering region grows in both directions at velocity v, while new points continue to form on uncovered parts of the interval. Eventually the whole interval will be covered. Let N ≧ 1 denote the total number of points formed. We derive integral expressions for E(N) and Var(N) and give precise asymptotic expressions for these moments as ρ = λ/v →∞. Asymptotic normality of N is also established.

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