Scan Statistics for Detecting a Local Change in Model Parameters for Normal Data

In this chapter, we review the testing procedures that have been investigated in the scientific literature for detecting a local change in the parameters of a normal distribution, for one- and two-dimensional data. In Chen and Glaz (2021), testing procedures for detecting a local change in the population mean for one-dimensional normal data have been reviewed, when the population variance is known. In this chapter we assume that both population mean and population variance are unknown. We also consider the case when a local change in the population mean and population variance occurs simultaneously. When the size of the local region where the change of the parameters has occurred is unknown, we consider testing procedures based on the minimum p-value statistic and the generalized likelihood ratio type statistic. Simulation algorithms and numerical results are presented to evaluate the accuracy of the specified significance level and the power of the test statistics discussed in this chapter. When the size of the local region where the change of the parameters has occurred is unknown, numerical results are presented to compare the power of the test statistics based on fixed and multiple window scan statistics.