English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper is concerned with the uniform CLT for an empirical estimator of countable state space semi-Markov processes indexed by functions under the uniformly integrable entropy condition. The results of this paper generalise those of Limnios [(2004), ‘A Functional Central Limit Theorem for the Empirical Estimator of a Semi-Markov Kernel’,  Journal of Nonparametric Statistics , 16(1–2), 13–18. The International Conference on Recent Trends and Directions in Nonparametric Statistics]. We apply our results to the following important topics: on the kernel-type estimator of the semi-Markov kernel, the weak convergence of the smoothed empirical semi-Markov processes, we introduce the copula estimators in the semi-Markov framework and we establish their limiting laws by using the functional delta methods. We prove the main results for the uniform CLT via a martingale difference sequence as in Bae et al. [(2010), ‘The Uniform CLT for Martingale Difference Arrays Under the Uniformly Integrable Entropy’,  Bulletin of the Korean Mathematical Society , 47(1), 39–51].

The uniform CLT for the empirical estimator of countable state space semi-Markov kernels indexed by functions with applications