On the Efficiency of the newly Proposed Convex Olanrewaju-Olanrewaju Lo-oλγ(|θ|) Penalized Regression-Type Estimator via GLMs Technique.

In this article, we proposed a novel convex penalized regression-type estimator, termed Olanrewaju-Olanrewaju penalized regression-type estimator, denoted by  Lo-oλγ(|θ|) for ultra and high-dimensional data consideration whenever the number of covariates (p) is strictly greater than the sample size(n⁡). The newly proposed penalized estimator was formulated via the unique combination of arctangent and hyperbolic functions. It was noted that the newly proposed estimator could efficiently work under the constraint pp. The proposed convex penalized regression-type estimator was formulated via three symmetric distributional noises of Gaussian, Laplace, and Normal Inverse Gaussian (NIG), considered being the three certified symmetric distributions that belong to the exponential family of distributions. The regularity axioms and oracle properties of the newly proposed penalized estimator were worked-out, as well as the parameter estimation for the penalized regression-type estimator for the three symmetric noises via canonical expressible form of Generalized Linear Models (GLMs) and first-order Karush-Kuhn-Tucker (KKT) condition. The Lo-oλγ(|θ|)  regression-type estimator was subjected to simulation studies of well-generated symmetric observations. The US Longley macroeconomic dataset with the constraint p