Robust estimation and outlier detection based on linear regression model

Abstract

Outlier detection has always been a more active research topic in statistical diagnosis. Outliers are ubiquitous at data analysis areas in current and may produce erroneous results. In multivariate linear regression model, the existence of outliers will directly affect the modeling, parameter estimation and prediction. A set of data contains abnormal values, which will have a great impact on the estimation of the mean and standard deviation of the data, and also affect the estimation results of the least squares method. In the paper, on the basis of the linear regression model and deleting model and mean shift model, from the perspective of residual sum of squares and by introducing sample quantile to estimate the overall parameters robustly, a special statistic which is combined with the sample quantile method is used to detected the outliers. Finally, an example is analyzed and compared with the traditional method. The results show that the method is more effective.