One-Step and Two-Step Estimation in a Time-Varying Parametric Model

• Activity Number: 522 - Recent Advances in Semiparametric Statistical Methods
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Bogdan Gadidov* and Mohammed Chowdhury and Brad Barney
• Companies: Kennesaw State University and Kennesaw State University and Brigham Young University
• Keywords: kernel smoothing; local polynomial smoothing; spline smoothing ; one-step and two-step estimation

Abstract

Since nonparametric smoothing plays a preeminent role in the estimation of time-varying parameters, it is important to explore and understand the properties of available estimation techniques. We consider the situation in which the response variable follows a parametric model indexed by a parameter that varies smoothly over time. The estimates are obtained via kernel, spline, and local polynomial smoothing. Furthermore, we compare one-step and two-step estimation techniques. The one-step approach directly produces smoothed estimates, while the two-step implementation first obtains raw parameter estimates on a grid of time values and then applies smoothing strategies to these raw quantities. We detail properties such as asymptotic biases, variances and the mean squared errors of some such estimators. Application of one-step and two-step smoothing procedures is demonstrated with large demographic studies. Additionally, we present a comparative simulation study that assesses one-step and two-step smoothing estimation in terms of bias, MSE and smoothing estimates.