Affiliation:
1. Department of Mathematical Sciences University of Copenhagen Copenhagen Denmark
2. Department of Actuarial Science, Faculty of Business and Economics University of Lausanne Bâtiment Extranef Lausanne Switzerland
Abstract
AbstractThe estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time‐homogeneous case is classic, the time‐inhomogeneous case has recently received increased attention due to its added flexibility and advances in computational power. However, commuting subintensity matrices are assumed, which in various cases limits the parsimonious properties of the resulting representation. This paper develops the theory required to solve the general case through maximum likelihood estimation, and in particular, using the expectation‐maximization algorithm. A reduction to a piecewise constant intensity matrix function is proposed in order to provide succinct representations, where a parametric linear model binds the intensities together. Practical aspects are discussed and illustrated through the estimation of notoriously demanding theoretical distributions and real data, from the perspective of matrix analytic methods.
Funder
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Subject
Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
1 articles.
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