Asymptotic inference for a change-point Poisson process. (English) Zbl 0648.62093

Akman, V. E.; Raftery, A. E.

Ann. Stat. 14, 1583-1590 (1986).

Easily implemented asymptotic off-line procedures for the change-point Poisson process with \(\lambda\) (t), the intensity at time t, equal to \(\lambda_ 1\) if \(t\leq \tau\) and to \(\lambda_ 2\) if \(t>\tau\), are developed. They may also be applied to a problem of estimation of the location of a discontinuity in density discussed by H. Chernoff and H. Rubin, Proc. 3rd Berkeley Sympos. Math. Stat. Probab. 1, 19-37 (1956; Zbl 0072.363).
A test for change is noted, a test of the hypothesis that \(\tau =\tau_ 0\) is proposed, and point and interval estimates of \(\tau\), \(\lambda_ 1\), and \(\lambda_ 2\) are provided. The small-sample performance of the proposed procedures is studied using simulation, and an example is given.

MSC:

62M02	Markov processes: hypothesis testing
62M05	Markov processes: estimation; hidden Markov models
62F12	Asymptotic properties of parametric estimators

Keywords:

coal-mining disasters; confidence interval; consistent estimator; discontinuous density; small-sample properties; asymptotic off-line procedures; change-point Poisson process; simulation

Citations:

Zbl 0072.363