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Concentration order on a metric space, with some statistical applications

✍ Scribed by Cheng Cheng; Y.L. Tong


Book ID
104303109
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
123 KB
Volume
44
Category
Article
ISSN
0167-7152

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✦ Synopsis


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-ΓΏt tests are shown as applications.


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