On the estimation of parameters of switched Poisson processes. (Russian) Zbl 0582.62076

Anisimov, V. V.

Teor. Veroyatn. Mat. Stat. 31, 3-12 (1984).

Let \((x(t),y_{\theta}(t))\), \(t\geq 0\), be a finite-dimensional stochastic process such that for a fixed trajectory of x(t), \(y_{\theta}(t)\) is a compound Poisson type process with an intensity \(\lambda\) (\(\theta\),x). The problem is to estimate the unknown parameter \(\theta\) on the basis of observations of the process \((x(t),y_{\theta}(t))\), \(t\in [0,T].\)
The author studies the ML-estimators of \(\theta\) and proves, under some conditions, that they are strongly consistent and asymptotically normal. He has found also the estimators based on the method of moments which are compared with the ML-estimators. Comments concerning related topics are given, too.

Reviewer: J.M.Stoyanov

MSC:

62M05

Markov processes: estimation; hidden Markov models

Keywords:

maximum likelihood estimators; compound Poisson type process; strongly consistent; asymptotically normal; method of moments