Medical Data for the Nadaraya-Watson Kernel Method in Nonparametric Regression Models Based on Hyperbolic Secant Function

Abstract

Nonparametric kernel estimates used in this work aim to compare different treatment options by examining the recorded medical data. The following use of the suggested strategy depends on a kernel function and a parameter called bandwidth. The Nadaraya-Watson kernel (NWK) estimation is a necessary nonparametric kernel estimator used in regression models. A new Nadaraya-Watson regression estimate depends on the hyperbolic secant kernel (HSK) with fixed bandwidth (FNW) and Variable Bandwidth (VNW) is proposed.. We calculated some properties of the unknown regression function estimator, including bias, variance, optimal bandwidth, and a global measure of error criterion mean square error. Finally, simulation and three real data sets are used to evaluate its performance. Results from simulation and real data showed that the VNW using HSK is more effective than the FNW based on Average Mean Square Error Criterion. Also, Nadaraya-Watson using HSK function is more effective than Nadaraya-Watson using the Gaussian kernel density function.