Development of Time Series Disorder Detection Algorithms Based on Nonparametric Hypothesis Testing Criteria

The solution of the problem of detecting, in the online mode, a spontaneous change in the probabilistic characteristics (“disorder” or “breakdown”) of a time series is given. It is pointed out that there is a growing interest in the development of so-called nonparametric disorder detection methods, i.e., methods the application of which does not require the knowledge of the probability distribution function of the controlled process values. It is stated that the majority of the known versions of such methods are based on using a number of standard nonparametric criteria transformed for solving disorder detection problems. It is proposed to use the signs criterion, the series criterion, and the Ramachandran–Ranganathan criterion as a basis for construction of disorder detection algorithms. The methodical aspects of studying the statistical properties and efficiency of the disorder detection algorithms built on their basis are considered. The simulation method was used as a study tool. The plan of carrying out simulation experiments was developed separately for each of the proposed algorithms, taking into account their individual characteristics, but based on the general requirement of fully reproducing the monitoring algorithm performance dynamics under real conditions, when a disorder can appear at any time and there is a transient in the values of the decisive function. By using a simulation experiment for each of the algorithms under consideration, data on their statistical characteristics were obtained and systematized in a scope sufficient for synthesizing a monitoring procedure with the specified properties.

Nonparametric Hypothesis Testing Report

This report is the brief survey of nonparametric hypothesis testing. It includes four main sections about hypothesis testing, one additional section discussing goodness-of-fit and conclusion section.Sign test section gives an overview of nonparametric testing, which begins with the test on sample median without assumption of normal distribution.Signed-rank test section and rank-sum test section concern improvements of sign test. The prominence of signed-rank test is to be able to test sample mean based on the assumption about symmetric distribution. Rank-sum test discards the task of assigning and counting plus signs and so it is the most effective method among ranking test methods.Nonparametric ANOVA section discusses application of analysis of variance (ANOVA) in nonparametric model. ANOVA is useful to compare and evaluate various data samples at the same time.Nonparametric goodness-fit-test section, an additional section, focuses on different hypothesis, which measure the distribution similarity between two samples. It determines whether two samples have the same distribution without concerning how the form of distribution is.The last section is the conclusion.Note that in this report terms sample and data sample have the same meaning. A sample contains many data points. Each data point is also called an observation.