Scan statistics for detecting a local change in variance for normal data with unknown population variance

作者：Zhao Bo^*; Glaz Joseph

来源：Statistics & Probability Letters, 2016, 110: 137-145.

DOI：10.1016/j.spl.2015.12.020

• Bootstrap test
• Generalized likelihood ratio test
• Minimum P-value statistic
• Moving sum of squares
• Multiple window scan
• Variable window scan

In this article we investigate the performance of fixed, multiple and variable window scan statistics in detecting a local change in variance for a sequence of normal observations, when the population variance of the underlying normal distribution is unknown. For fixed window scan statistics, we study: the training sample approach, the conditioning on sufficient statistic approach and the parametric bootstrap testing approach. It is evident from the numerical results that the scan statistic constructed via the conditioning approach outperforms the other two fixed window scan statistics investigated in this article. Based on power calculation presented in this article, one can conclude that when the size of the window where a local change of variance has occurred is unknown, multiple and variable window scan statistics outperform fixed window scan statistics. The multiple and variable window scan statistics perform equally well. When the sequence of observations is large, the implementation of the multiple window scan statistic is computationally more practical.

• 出版日期2016-3