Theoretical Mathematics & Applications

Robust Test for detecting Outliers in Periodic Processes using Modified Hampelís Statistic

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  • Abstract

     

     

    It is generally difficult to identify the exact outliers in periodic process and the suitable outlier detection method without a given underlying outlier process; also important is to discover the unusual data whose behavior is very exceptional when compared to the rest of the data set since the presence of the outlier can mar the model characterization techniques. Hampel suggested an identifier using the median to estimate data location and median absolute deviation to estimate the standard deviation. We apply the Modified Hampel Statistics by introducing the Jacknife method to the estimation of the parameters needed in Hampel detecting method to robust estimates. The two methods considered are implemented on-line and off-line points in finite samples taken for both real-life and simulated data using PAR (I) model. The results in both cases show that the Modified Hampel Statistic has higher rate of outlier identification for on-line detection. However, all the points identified by the Hampel method are also confirmed by the new Robust Hampel Method. The robust method identified less off-line points than the Hampel Method, this further shows the effectiveness of our robust method in an attempt to reject off-line points that are falsely identified by Hampel method as outliers.