A Comparison of Autometrics and Penalization Techniques under Various Error Distributions: Evidence from Monte Carlo Simulation

This work compares Autometrics with dual penalization techniques such as minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) under asymmetric error distributions such as exponential, gamma, and Frechet with varying sample sizes as well as predictors. Comprehensive simulations, based on a wide variety of scenarios, reveal that the methods considered show improved performance for increased sample size. In the case of low multicollinearity, these methods show good performance in terms of potency, but in gauge, shrinkage methods collapse, and higher gauge leads to overspecification of the models. High levels of multicollinearity adversely affect the performance of Autometrics. In contrast, shrinkage methods are robust in presence of high multicollinearity in terms of potency, but they tend to select a massive set of irrelevant variables. Moreover, we find that expanding the data mitigates the adverse impact of high multicollinearity on Autometrics rapidly and gradually corrects the gauge of shrinkage methods. For empirical application, we take the gold prices data spanning from 1981 to 2020. While comparing the forecasting performance of all selected methods, we divide the data into two parts: data over 1981–2010 are taken as training data, and those over 2011–2020 are used as testing data. All methods are trained for the training data and then are assessed for performance through the testing data. Based on a root-mean-square error and mean absolute error, Autometrics remain the best in capturing the gold prices trend and producing better forecasts than MCP and SCAD.

Penalized Likelihood Estimation of Gamma Distributed Response Variable via Corrected Solution of Regression Coefficients

A Gamma distributed response is subjected to regression penalized likelihood estimations of Least Absolute Shrinkage and Selection Operator (LASSO) and Minimax Concave Penalty via Generalized Linear Models (GLMs). The Gamma related disturbance controls the influence of skewness and spread in the corrected path solutions of the regression coefficients.

Non-Convex Penalized Estimation of Count Data Responses via Generalized Linear Model (GLM)

This study provided a non-convex penalized estimation procedure via Smoothed Clipped Absolute Deviation (SCAD) and Minimax Concave Penalty (MCP) for count data responses to checkmate the problem of covariates exceeding the sample size . The Generalized Linear Model (GLM) approach was adopted in obtaining the penalized functions needed by the MCP and SCAD non-convex penalizations of Binomial, Poisson and Negative-Binomial related count responses regression. A case study of the colorectal cancer with six (6) covariates against sample size of five (5) was subjected to the non-convex penalized estimation of the three distributions. It was revealed that the non-convex penalization of Binomial regression via MCP and SCAD best explained four un-penalized covariates needed in determining whether surgical or therapy ideal for treating the turmoil.