Nonparametric Estimation of Time-Variant Parametric Models with Application to Cross-Sectional Data

Abstract

In this article, two estimation approaches based on age-specific parametric model have been proposed and a comparative study between them has been studied. We assume that outcome variable follows a parametric model, but the parameters are smooth function of time (age). Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the parameters at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. We derived asymptotic properties such as asymptotic biases, variances and mean squared error (MSE) for the local polynomial smoothed estimator and kernel smoothing estimator for the parameter of the time-variant parametric model. A mathematical relationship is established between two asymptotic MSEs. Mathematical relationship between two smoothing estimators has also been established. Applications of our two-step estimation method have been demonstrated through a large demographic study to estimate fecundability. Theoretical results on coverage of bootstrap confidence intervals for these smoothing estimators have been derived. Finite sample properties of our procedures are investigated by a simulation study.