Two-step Smoothing Estimation of the Time-variant Parameter with Application to Temperature Data

‎In this article‎, ‎we develop two nonparametric smoothing estimators for parameter of a time-variant parametric model‎. ‎This parameter can be from any parametric family or from any parametric or semi-parametric regression model‎. ‎Estimation is based on a two-step procedure‎, ‎in which we first get the raw estimate of the parameter at a set of disjoint time points and then compute the final estimator at any time by smoothing the raw estimators‎. ‎We will call these estimators two-step local polynomial smoothing estimator and two-step kernel smoothing estimator‎. ‎We derive these two two-step smoothing estimators by modeling raw estimates of the time-variant parameter from any regression model or probability model and then establish a mathematical relationship between these two estimators‎. ‎Our two-step estimation method is applied to temperature data from Dhaka‎, ‎the capital city of Bangladesh‎. ‎Extensive simulation studies under different cross-sectional and longitudinal frameworks have been conducted to check the finite sample MSE of our estimators‎. ‎Narrower bootstrap confidence bands and smaller MSEs from application and simulation results show the superiority of the local polynomial smoothing estimator over the kernel smoothing estimator‎.