Statistics and Its Interface
Volume 12 (2019)
Hybrid Graphical Least Square Estimation and its application in Portfolio Selection
Pages: 631 – 645
This paper proposes a new regression method based on the idea of graphical models to deal with regression problems with the number of covariates v larger than the sample size $N$. Unlike the regularization methods such as ridge regression, LASSO and LARS, which always give biased estimates for all parameters, the proposed method can give unbiased estimates for important parameters (a certain subset of all parameters). The new method is applied to a portfolio selection problem under the linear regression framework and, compared to other existing methods, it can assist in improving the portfolio performance by increasing its expected return and decreasing its risk. Another advantage of the proposed method is that it constructs a non-sparse (saturated) portfolio, which is more diversified in terms of stocks and reduces the stock-specific risk. Overall, four simulation studies and a real data analysis from London Stock Exchange showed that our method outperforms other existing regression methods when $N \lt v$.
Graphical Model, Graphical Least Squares, LASSO, Ridge Regression, Unbiased Estimation
Dr. Zhang is supported by the National Natural Science Foundation of China (Grant No.11601244).
Received 8 June 2018
Received revised 16 March 2019
Accepted 20 May 2019
Published 18 July 2019