Enhancing Kernel Estimators Using the Hyperbolic Secant Kernel for Nonparametric Regression: Applications to Simulation and Real Data

Abstract

In this study, we rely on adaptive kernel estimation to improve the non-parametric estimation of the probability density function (pdf) using the hyperbolic secant kernel (HSK). Previous research has demonstrated that adaptive kernel estimators with diverse and different bandwidths yield superior performance. This paper introduces an enhancement to the hyperbolic secant kernel estimator (HSKE) through the use of Quartile Deviation (QD), Coefficient of Variation (CV), and Variance-to-Mean Ratio (VMR). These proposed methods have also been applied to nonparametric Nadaraya-Watson (NW) regression. The mean squared error (MSE) is a measure used to evaluate the performance the new estimators that have been suggested. A lower MSE indicates a more accurate estimator or model, reflecting its effectiveness in making precise predictions. The simulation study results showed that very positive results, demonstrating that our modification of HSKE shows good performance in all cases. The two real data sets are showed improvement in the regression model when using the new methods