Analysis of a signal starting time estimator based on the Page test statistic

Many signal processing applications require the detection of an abrupt change with subsequent estimation of the actual time of occurrence of the change. The time of the most recent reset to zero of the Page test statistic is proposed for this purpose. The probability mass function of the estimator is determined analytically subject to a quantization of the Page test statistic update. Closed-form results for the first three uncorrected moments of the estimator are presented. The analytical results are verified by comparison to simulation results and the fineness of the quantization required for accurate representation is investigated by evaluation of the Kolmogorov-Smirnov statistic. The bias, standard deviation, and skewness of the estimator as a function of the signal strength and detector threshold are evaluated for Gaussian shift-in-mean and noncentral chi-squared changes in signal type.