ASSESSMENT OF POWER OF SOME NON-PARAMETRIC TREND CRITERIA
DOI:
https://doi.org/10.32782/KNTU2618-0340/2020.3.2-1.17Keywords:
time series; trend criteria; criterion power; statistical modeling; diagnosticsAbstract
An approach to the selection and comparison of criteria that are used in the analysis of time series of parameters for recording the technical condition of complex technical objects is proposed. The approach is based on established important characteristics of trending criteria, namely the power of such criteria, which are considered as criteria for distinguishing complex hypotheses. For analysis, we propose a statistical model for generating data in the form of a combination of deterministic trend and random components. The deterministic component is considered as a linear approximation of its expansion in a Taylor series. This assumption is justified by the need to identify a trend in the shortest period of time at which the trend component allows a linear approximation. The random component is taken in the form of a sample from the general population of independent random variables that have a normal distribution. For analysis, the most common nonparametric trend criteria were selected: Wald-Wolfowitz criterion; Bartles test; inversion criterion; as well as a parametric correlation criterion for comparison. The support hypothesis has the form of belonging of a time series to a sample from the general set of independent random variables, and an alternative is belonging to a sample with a linear trend. Trend statistics of the relevant criteria are generated on a sliding or sectional disjoint analysis window of a given dimension. The trend development parameter was selected as the ratio of the trend growth during the analysis to the standard deviation of the random component. For the considered trend criteria, the dependences of their power on the trend development parameter and the probability of an error of the first kind (erroneous alarm), as well as operational characteristics of the criteria, are obtained. The analysis was carried out by methods of analytical estimates and statistical modeling. It has been established that in the case of an alternative, the statistics of the analyzed criteria are normalized, and the statistics of the correlation criterion do not change their type. A comparison of trending power criteria with equal values of the probability of an error of the first kind allows us to establish the advantage of the inversion criterion, and the criterion has the worst performance. Walda-Wolfowitz. Estimating the power of trend criteria is important for applied applications, since it allows you to establish the probability of a second kind of error (skipping a trend).
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