Statistical estimation of jump rates for a specific class of Piecewise Deterministic Markov Processes

2014/06/11 by Krell, Nathalie
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1406.2845

Abstract

We consider the class of Piecewise Deterministic Markov Processes (PDMP), whose state space is \R_+^*, that possess an increasing deterministic motion and that shrink deterministically when they jump. Well known examples for this class of processes are Transmission Control Protocol (TCP) window size process and the processes modeling the size of a "marked" \it Escherichia coli cell. Having observed the PDMP until its nth jump, we construct a nonparametric estimator of the jump rate λ. Our main result is that for D a compact subset of \R_+^*, if λ is in the H''older space \mathcal H^s(\mathcal D), the squared-loss error of the estimator is asymptotically close to the rate of n^-s/(2s+1). Simulations illustrate the behavior of our estimator.

Related

• Nonparametric estimation of jump rates for a specific class of Piecewise Deterministic Markov Processes
• Asymptotic Analysis and Practical Evaluation of Jump Rate Estimators in Piecewise-Deterministic Markov Processes
• A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions
• Optimal choice among a class of nonparametric estimators of the jump\n rate for piecewise-deterministic Markov processes
• Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes