We derive some limit theorems associated with the Ewens sampling formula when its parameter is increasing together with a sample size.
Moreover, the limit results are applied in order to investigate asymptotic properties of the maximum likelihood estimator.
Functional central limit theorems in L 2 (0, 1) for logarithmic combinatorial assemblies are presented. The random elements argued in this paper are viewed as elements taking values in L 2 (0, 1) whereas the Skorokhod space is argued as a framework of weak convergences in functional central limit theorems for random combinatorial structures in the literature. It enables us to treat other standardized random processes which converge weakly to a corresponding Gaussian process with additional assumptions.
A test procedure based on continuous observation to detect a change in drift parameters of an ergodic diffusion process is proposed. The asymptotic behavior of a random field relating to an estimating equation under the null hypothesis is established using weak convergence theory in separable Hilbert spaces. This result is applied to a change point detection test.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.