According to the above analysis, under the minimum maximization criterion, Huber M estimation and median estimation are the two most robust and optimal measures; Huber M estimation can reflect the characteristics of statistics, and has continuous, non-decreasing, bounded, and With zero-centered and odd function characteristics, it is difficult to realize in actual data processing; median estimation can reflect the location characteristics, but not the overall data characteristics.

The method of determining the data range is based on the order statistics of the sample, the median is the data center, and the maximum and minimum values ​​are assumed to be discrete values. These data contain discrete data, so the order statistics can't identify discrete data and can't perform robust data processing. This method is to first replace the maximum and minimum values ​​with their adjacent data to obtain new data; then calculate the average of the new data.

The closer the average is to the median, the more robust the data. Based on the above-mentioned data robustness processing ideas, the order statistics of L estimation are used to sort the data. If the average of the new data is closer to the median than the average of the original data, it means that the new data is more robust than the original data. Among them, the simple replacement type is a simple and effective discrete value processing method. This shows that the data is the most robust data.

The closer the average is to the median, the more robust the data; otherwise, the less robust the data. In the process of data robustness processing, there are three types of discrete value processing methods, namely replacement, addition, and simple replacement. Using the principle of Huber m estimation, when the data exceeds a certain range, it is considered as a discrete value, and these data are replaced by the critical value of the data range. However, discrete data has a great influence on the average value of the data, making the average value unstable.

Therefore, combining the two estimation characteristics, combined with the L estimation idea, this chapter proposes a new robust processing method to achieve better performance of the robust processing of experimental data. First, the minimum and maximum values ​​are successively replaced with adjacent data to obtain improved data;. Due to the influence of discrete data, the average value of the data is not robust. Therefore, the closeness of the average to the median can reflect the robustness of the data.

In order to prevent reducing the sample size, the method of processing discrete data adopts the Huber m method. Use this method in turn Mechanical ball bearings manufacturers to get the new data until the average of the new data is closest to the median. The robustness of the median can be used as a criterion for the robustness of the average. Generally speaking, in the process of data robustness processing, there is a significant level requirement. According to the robust statistical theory of modern statistics, the median of the data is robust

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