基于统计分布信息的上市公司随机缺失数据的KNN插补

KNN Imputation of Random Missing Data of Listed Companies Based on Statistical Distribution Information

数据缺失会为上市公司财务状况分析带来挑战。上市公司财务数据是兼具横截面和时间两个维度的面板数据,包含更多的统计分布信息。本文分别从多项式流形、参数假设检验、信息量3个视角,提出基于Cosine距离、HotellingT^(2)统计量、Jensen-Shannon散度的3种KNN插补法,并对2021年第3季度至2022年第一季度的财务数据随机缺失状态下的插补性能进行验证。结果表明,缺失率较低时,Cosine距离的插补性能最优;缺失率较高时,HotellingT^(2)度量的插补性能最好。

Missing data will bring challenges to the analysis of the financial conditions of listed companies.The financial data of listed companies is a panel data of both cross-section and time dimensions,containing more statistical distribution information.This paper proposes three k-nearest neighbor imputation methods based on Cosine distance,HotellingT^(2) statistic and Jensen-Shannon divergence,from the perspectives of polynomial manifold,parameter hypothesis test and information quantity,and verifies the interpolation performance in the random missing state of financial data from the third quarter of 2021 to the first quarter of 2022.The results show that when the missing rate is low,the imputation performance of the Cosine distance is the best;when the missing rate is high,the imputation performance of the HotellingT^(2) measure is the best.