The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity +v or -v. The changes of direction are governed by a homogeneous Poisson process with rate lambda > 0. In this paper, we consider a change-point estimation problem for the rate of the underlying Poisson process by means of the least-squares method under the hypothesis of discrete-time sampling. Consistency, rate of convergence and distributional results for the change-point estimator are obtained under both fixed and random sampling. An application to real data is presented.

Least-squares change-point estimation for the telegraph process observed at discrete times / DE GREGORIO, Alessandro; Stefano M., Iacus. - In: STATISTICS. - ISSN 0233-1888. - 45:4(2011), pp. 349-359. [10.1080/02331881003769022]

Least-squares change-point estimation for the telegraph process observed at discrete times

DE GREGORIO, ALESSANDRO;
2011

Abstract

The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity +v or -v. The changes of direction are governed by a homogeneous Poisson process with rate lambda > 0. In this paper, we consider a change-point estimation problem for the rate of the underlying Poisson process by means of the least-squares method under the hypothesis of discrete-time sampling. Consistency, rate of convergence and distributional results for the change-point estimator are obtained under both fixed and random sampling. An application to real data is presented.
2011
change-point problem; discrete observations; random times; telegraph process
01 Pubblicazione su rivista::01a Articolo in rivista
Least-squares change-point estimation for the telegraph process observed at discrete times / DE GREGORIO, Alessandro; Stefano M., Iacus. - In: STATISTICS. - ISSN 0233-1888. - 45:4(2011), pp. 349-359. [10.1080/02331881003769022]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/140255
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