## The Annals of Statistics

### Nonparametric Inference for a Class of Semi-Markov Processes with Censored Observations

#### Abstract

A class of semi-Markov models, those which have proportional hazards and which are forward-going (if state $j$ can be reached from $i$, then $i$ cannot be reached from $j$), are shown to fit into the multiplicative intensity model of counting processes after suitable random time changes. Standard large-sample results for counting processes following this multiplicative model can therefore be used to make inferences on the above class of semi-Markov models, including the case where observations may be censored. Large-sample results for a four-state model used in clinical trials are presented.

#### Article information

Source
Ann. Statist., Volume 12, Number 1 (1984), 142-160.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346398

Digital Object Identifier
doi:10.1214/aos/1176346398

Mathematical Reviews number (MathSciNet)
MR733505

Zentralblatt MATH identifier
0552.62020

JSTOR