Scan Statistics for Detecting a Local Change in Variance for Normal Data with Known Variance

In this article, several scan statistics are discussed for detecting a local change in variance for one dimensional normal data. When the length of the scanning window is known, a fixed window scan statistic based on moving sum of squares is proposed. Two approximations for the distribution of this scan statistic are investigated. When the length of the scanning window is unknown, a variable window scan statistic based on a generalized likelihood ratio test and a multiple window minimum P-value scan statistic are proposed for detecting the local change in variance. For a moderate or large shift in variance, numerical results indicate that both the variable and multiple window scan statistics perform well. For large data sets, considering the detection power and computing efficiency, the multiple window scan statistic is recommended.