Applied Research Of Robust MM Estimation In Interval-valued Data

In recent years,due to the increasing complexity of data,such as diverse data types,large amount of data,outliers in the data,incomplete data,etc.,interval value data has become more and more common in problem analysis.Interval valued data is a type of data in which each feature is an interval,because this type of data represents either the uncertainty present in the error measurement or the natural variability present in the data.So it is widely used in practical situations,such as recording the daily interval temperature of weather stations,daily interval stock prices and so on.The commonly used interval estimation methods include interval least squares estimation,interval robust M estimation and interval exponential kernel robust regression estimation.Interval least squares estimation has become an effective mathematical method,which has been widely used in many professional aspects such as error estimation,uncertainty measurement,system identification and prediction,forecast and big data analysis and processing.However,the interval least square estimation is sensitive to the outliers in the data,and its estimation of the interval data is not robust.Interval robust M estimation only weights the direction of the dependent variable,but not the direction of the independent variable.Therefore,it can not handle the situation of outliers in the direction of interval valued data well.When there are few outliers in the interval valued data,the interval exponential kernel robust regression estimation has a good fit to the interval valued data.However,it is not a good fit for the large number of outliers in the interval value data of 30% or more.Based on interval least square estimation,interval robust M estimation and interval exponential kernel robust regression estimation all have their own shortcomings,so we apply robust MM estimation to interval value regression,put forward the interval robust MM estimation,and introduce the interval robust MM estimation algorithm in detail.Interval least square estimation,interval robust M estimation,interval exponential kernel robust regression estimation and interval robust MM estimation are applied to two-dimensional simulation interval value data.Monte Carlo simulation was used to consider spatial outliers,spatial outliers,spatial and spatial both outliers,and different percentage scenarios of outliers in the interval value data.Several interval robust estimates are analyzed based on the absolute median deviation and mean square error.The results show that under different outlier scenarios,the results of interval robust MM estimation are better than those of interval least square estimation,interval robust M estimation and interval exponential kernel robust regression estimation.We also apply several interval robust estimates to the two real interval value data.First,we verify the existence of outliers in the real interval value data by using the outlier test standard.Next,several interval robust estimates are compared and analyzed based on the mean square error,mean absolute error and mean absolute percentage error.The results still show that interval robust MM estimation can better solve the problem of interval data with outliers.The test is used to test the results of the simulated interval value data measure by comparing whether there are differences between interval least square estimation,interval robust M estimation,interval exponential kernel robust regression estimation and interval robust MM estimation.The test results show that under different outlier scenarios,The difference between interval estimation and interval robust MM estimation is also different.Whether the interval least square estimation,interval robust M estimation,interval exponential kernel robust regression estimation and interval robust MM estimation are applied to two-dimensional simulation interval value data,or several interval robust estimates are applied to real interval value data,the results can show that when there are outliers in interval value data,The interval robust MM estimates presented by us show good robustness.