Improvement And Application Of Outlier Detection Methods

With the development and progress of science,the discrete observed data may be dynamic and continuous potentially,with displaying certain functional feature,most of them usually appear as continuous functions or curves,which are called functional data.The essence of functional data analysis(FDA)is to treat the observed data as elements on the function.FDA is widely applied in various fields,such as Economic,Finance,Medical science and Meteorology,etc.Outliers mean that the observations in the sample significantly deviate from most of the other observations,which are different from the characteristics or structure of most of the other observations.The outlier has a great impact on the accuracy and dynamics of the data,and affect the analysis and modeling of the data.Therefore,in applications,outlier information can be mined,the causes and phenomena behind it can be analyzed,the corresponding suggestions can be made.Therefore,the detection and treatment of outliers have research value.This paper proposes a new functional depth,half-space depth in the reproducing kernel Hilbert space(RKHS),based on the Tukey half-space depth,expanding the calculation space,combined with the reproducing kernel.The related calculation method is introduced.The new functional depth is applied to realistic analysis.Moreover,this paper discusses the methods of functional outlier detection,including methods based on functional depths,functional principal component analysis,and functional directional outlyingness.In the realistic analysis,three types of functional outlier detection methods are applied to the Jiangxi resident electricity consumption data.In different research perspectives,the different functional outlier detection methods are compared,which shows the feasibility of the functional outlier detection method in realistic data.At the same time,it proposes that the outlier detection analysis of resident electricity consumption data can be applied to the implementation of the Minimum Living Security System.The proposal of the half-space depth in the regeneration kernel Hilbert space is an expansion in the field of the depth function and it enriches the functional outlier detection method.Through outlier detection analysis of resident electricity consumption data,it proposes that considering the potential misinsurance and leakage phenomena of the Minimum Living Security System,the rate of misinsurance and leakage can be reduced to a certain extent,the identification of rescue target can be more accurate,it provides a new path to improve the targeting rate of the Minimum Living Security System.In addition,outliers of resident electricity consumption data can be associated with measuring equipment problems,user theft,and differences in resident types.To sum up,the outlier detection analysis of Jiangxi resident electricity consumption data has certain theoretical and practical significance.