Asymptotic behaviour of a test statistic for detection of change in mean of vectors

作者：Jaruskova Daniela^*

来源：Journal of Statistical Planning and Inference, 2010, 140(3): 616-625.

DOI：10.1016/j.jspi.2009.08.004

• Change point detection
• Vectors with correlated components
• Multivariate partial cumulative sum process
• Extremal behaviour of a linear combination of standardized Brownian bridges

The paper gives an asymptotic distribution of a test statistic for detecting a change in a mean of random vectors with dependent components. The studied test statistic has a form of a maximum of a square Euclidean norms of vectors with components being standardized partial cumulative sums of deviations from means. The limit distribution was obtained using a result of Piterbarg [1994. High deviations for multidimensional stationary Gaussian processes with independent components. In: Zolotarev, V.M. (Ed.), Stability Problems for Stochastic Models, pp. 197-210].

• 出版日期2010-3