Concentration order on a metric space, with some statistical applications

Cheng Cheng and Y. L. Tong

Statistics & Probability Letters, 1999, vol. 44, issue 4, 327-335

Abstract: A concept called concentration order of probability distributions on a metric space is introduced, then the norm stochastic order that compares real-parameter stochastic processes is introduced as a special case. Equivalent conditions of concentration order are established. Using Anderson's theorem, norm stochastic orders of certain processes with almost-sure continuous sample paths are established, including Wiener processes and Brownian bridges as special cases. Limiting power monotonicity of some goodness-of-fit tests are shown as applications.

Keywords: Concentration; order; Stochastic; order; Norm; stochastic; order; Wiener; process; Brownian; bridge; Goodness; of; fit (search for similar items in EconPapers)
Date: 1999
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