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Title: Goodness-of-fit tests for Markovian processes based on marked empirical processes Authors:  Koji Tsukuda - The University of Tokyo (Japan) [presenting]
Yoichi Nishiyama - Waseda University (Japan)
Abstract: Weak convergences of marked empirical processes in $L^2(\mathbb{R},\nu)$ and their applications to statistical goodness-of-fit tests are provided, where $L^2(\mathbb{R},\nu)$ is the set of equivalence classes of the square integrable functions on $\mathbb{R}$ with respect to a finite Borel measure $\nu$. The results obtained in our framework of weak convergences are, in the topological sense, weaker than those in previous works. However, our results have the following merits: (1) avoiding conditions which do not suit for our purpose; (2) treating a weight function which make us possible to propose an Anderson--Darling type test statistics for goodness-of-fit tests. Indeed, applications are novel.