In this paper, weak convergences of marked empirical processes in L2\(R,ν\) and their applications to statistical goodness-of-fit tests are provided, where L2\(R,ν\) is the set of equivalence classes of the square integrable functions on R with respect to a finite Borel measure ν. The results obtained in our framework of weak convergences are, in the topological sense, weaker than those in the Skorokhod topology on a space of cádlág functions or the uniform topology on a space of bounded functions, which have been well studied 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 makes us possible to propose an Anderson–Darling type test statistics for goodness-of-fit tests. Indeed, the applications presented in this paper are novel.
|Publication status||Published - Aug 17 2018|
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