Change point detection is widely used in signal detection, industrial engineering, economy, finance, biomedicine and many other fields. The widely used parametric methods require prior knowledge of the noise signal distribution, which are seldom realistic. In practice, when the distribution of noise is not known, it is desirable to design algorithms based on non-parametric statistics, which, in the null case (no change point), are completely distribution free. To this end, we propose to use two symmetric sliding windows to compute the Area Under the receiver operating characteristic Curve (AUC) as a test statistic to measure the difference between the distribution of two samples. In the stage of change point detection, a threshold is designed according to hypothesis test which is based on the null distribution of the test statistics. This threshold is used to detect the potential change points in the signal. To reduce the probability of false alarm detection, a key parameter K is set to distinguish and delete the false alarms in potential change points. Comparative studies showed that our proposed method outperforms the classical Relative unconstrained Least-Squares Importance Fitting (RuLSIF) algorithm and is also better than the Hawkins, Qiu, and Kang (HQK) algorithm when the noise follows non-normal distributions.

Receiver operating characteristic (ROC) analysis has become an indispensable tool in medical care, with a major application to characterizing the performance of binary diagnostic tests in clinical practice. In many circumstances, however, the diagnostic test has three outcomes, that is, the abnormalities are two-sided. To deal with this scenario, this paper develops a recursive algorithm for computing the exact null distribution of the volume under the ordered three-class receiver operating characteristic surface (VUS) for samples following continuous distributions. Based on the asymptotic normality, an approximately normal distribution with exact mean and variance is also proposed, which is hoped to be useful for large-sample scenarios. Moreover, an efficient rank-based formula, in linearithmic time, is established for nonparametric estimation of VUS. Monte Carlo simulations verify the usefulness of the theoretical and algorithmic findings in this work.

Receiver operating characteristic (ROC) analysis has been widely used in two-class problems. However, in practice, three-class problems are frequently encountered, especially in the area medicine. To evaluate the performance of three-class classifiers, researchers have proposed the volume under the three-class ROC Surface (VUS) as a figure-of-merit. Unfortunately, however, all the existing methods suffer heavy computational loads, to the best of our knowledge. To overcome such an unsatisfactory problem, in this paper we develop an efficient dynamic programming based algorithm for unbiased estimation of VUS and the corresponding variance. Monte Carlo simulations verified both the unbiasedness and computing efficiency of our algorithm compared with the state-of-the-art work proposed byWaegeman and co-authors.