Single-Index ESL Robust Regression and Application

Robust regression has been a common method used to solve some portfolio selection problem by using traditional ordinary least square estimation (OLS). However, the outliers in the realistic data often break the data consistency rules which make the ordinary least square estimation lose efficacy. Here, the Exponential Squared Loss (ESL) robust regression is considered to eliminate the influence of outliers. By adjusting the square loss function into ESL function and adaptive LASSO penalty function, the parameters estimation accuracy is improved thereby, reducing the impact of outliers in historical returns on the investment portfolio decision. This article attempts to verify the robustness of the single index model by using Shenzhen A-share market data. The result indicates the advantage of the ESL robust regression by comparing the estimation accuracy of the ESL robust estimation with OLS estimation and M-estimation. Finally, the portfolio efficient frontier reveals the stability of ESL robust regression in the single index modeInt.