On the Theory and Pliability of Regressogram Decomposition: Application and Simulation Sensitivity of the Olanrewaju-Olanrewaju Kernel-Based Regressogram

This paper studies the pliability of regressogram decomposition as a technique of modeling bivariate random measurements of (X_1,Y_1),…,(X_n,Y_n) either via equal-width bins or linear smoother with the use of nonparametric, Olanrewaju-Olanrewaju, and machine-learning Boxcar kernels. The nonparametric, Olanrewaju-Olanrewaju, and Boxcar kernels were differently incorporated into the Nadaraya-Watson kernel-estimator as a generalized Mercer kernel. The optimal bandwidth needed as a smoothing parameter for impelling the kernel-based regressogram was derived with the aid of Generalized Cross-Validation (GCV). Finite and countable sample size bound required for the regressogram modeling was ascertained for reasonable sample sizes needed for effective optimization of coefficients, and deductive measurable of some error indexes via strongly universally consistent estimator. In conclusion, the Olanrewaju-Olanrewaju kernel-based regressogram was notably sensitive with the smallest magnitude of scale estimated (σ^2) and GCV estimates in application to real life dataset and simulation study to the nonparametric Doppler regression function.