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

ýIn this articleý, ýwe develop two nonparametric smoothing estimators for parameter of a time-variant parametric modelý. ýThis parameter can be from any parametric family or from any parametric or semi-parametric regression modelý. ýEstimation is based on a two-step procedureý, ýin 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 estimatorsý. ýWe will call these estimators two-step local polynomial smoothing estimator and two-step kernel smoothing estimatorý. ýWe 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 estimatorsý. ýOur two-step estimation method is applied to temperature data from Dhakaý, ýthe capital city of Bangladeshý. ýExtensive simulation studies under different cross-sectional and longitudinal frameworks have been conducted to check the finite sample MSE of our estimatorsý. ýNarrower bootstrap confidence bands and smaller MSEs from application and simulation results show the superiority of the local polynomial smoothing estimator over the kernel smoothing estimatorý.