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Least-squares change-point estimation for the telegraph process observed at discrete times
- Publication Year :
- 2011
- Publisher :
- TAYLOR & FRANCIS LTD, 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 λ>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.
- Subjects :
- Statistics and Probability
Mathematical optimization
Discrete Poisson equation
Mathematical analysis
Sampling (statistics)
Estimator
telegraph process
change-point problem
discrete observations
random times
Least squares
Point process
symbols.namesake
Rate of convergence
Compound Poisson process
symbols
Statistics, Probability and Uncertainty
Telegraph process
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....426032fa2beff1138da4b3fda4697d8a