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
• DOI: 10.1016/s0167-7152(99)00023-1

✦ 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-ÿt tests are shown as applications.