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Rényi-type empirical processes

Miklós Csörgo and Lajos Horvath

Journal of Multivariate Analysis, 1992, vol. 41, issue 2, 338-358

Abstract: We develop a theory of asymptotics for Rényi-type weighted empirical and quantile processes and statistics via characterising their possible limiting behaviour in the middle and on the tails. In case of moderate weight functions tail limiting behaviour is found to be Gaussian, while heavily weighted tail empirical and uniform quantile processes are characterised by their respective Poisson process and exponential sums like asymptotic behaviour.

Keywords: Renyi-type; statistics; weighted; empirical; and; uniform; quantile; processes; weak; weighted; approximations; Wiener; Poisson; and; exponential; sums; processes; tail; behaviour; of; Poisson; processes; Kac-Poisson; bridge (search for similar items in EconPapers)
Date: 1992
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Handle: RePEc:eee:jmvana:v:41:y:1992:i:2:p:338-358