Abstract

Semiparametric Single Index Models are important and essential tools for addressing the highdimensional problem, as they play an important role in the model-building process and selecting marginal variables. In this research, some modern penal methods have been used, which assess the vector of parameters and simultaneously select the variable for the quasi-parameter single indicator models (MAVE-LASSO) and MAVE Elastic net) to improve the accuracy and predictability of the model. In order to achieve this goal, simulation experiments were conducted to demonstrate the preferences of the methods used in estimating and selecting the variable for the model. Different models, different variations, different sample sizes, and real data of factors influencing patients with blood diabetes were used for comparison and verification of the performance of these methods in practice. The methods studied will be compared by relying on two benchmarks for comparison: the average mean square error (AMSE) and the absolute average mean square error (AMAE), and the results will be obtained based on the R-code. Theoretically and simulation-wise, the MAVE-EN method for estimating and selecting important variables for a single-indicator semi-parametric model has been shown to be effective in dealing with cases of high correlation between explanatory variables in the presence of different variances.