Statistics and Its Interface

Volume 12 (2019)

Number 4

Hybrid Graphical Least Square Estimation and its application in Portfolio Selection

Pages: 631 – 645



Saeed Aldahmani (Department of Statistics, College of Business and Economics, United Arab Emirates University, U.A.E.)

Hongsheng Dai (Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom)

Qiaozhen Zhang (School of Statistics and Data Science, Nankai University, Tianjin, China)


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