Nonparametric tests for transition probabilities in nonhomogeneous Markov processes

Giorgos Bakoyannis

Journal of Nonparametric Statistics, 2020, vol. 32, issue 1, 131-156

Abstract: This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time nonhomogeneous Markov process with a finite state space. The proposed tests are a linear nonparametric test, an $ L^2 $L2-norm-based test and a Kolmogorov–Smirnov-type test. Significance level assessment is based on rigorous procedures, which are justified through the use of modern empirical process theory. Moreover, the $ L^2 $L2-norm and the Kolmogorov–Smirnov-type tests are shown to be consistent for every fixed alternative hypothesis. The proposed tests are also extended to more complex situations such as cases with incompletely observed absorbing states and non-Markov processes. Simulation studies show that the test statistics perform well even with small sample sizes. Finally, the proposed tests are applied to data on the treatment of early breast cancer from the European Organization for Research and Treatment of Cancer (EORTC) trial 10854, under an illness-death model.

Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1080/10485252.2019.1705298 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:gnstxx:v:32:y:2020:i:1:p:131-156

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485252.2019.1705298

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().