Online Program

Nonparametric Estimation of Time-Variant Quantiles and Statistical Models (303587)

 View Presentation

Keywords: logitudinal, nonparametric, spline, kernel, local polynomial, quantiles,

We consider probability and regression models as well as nonparametric estimates of quantiles from functional data for smoothing estimation. We develop the estimation procedure in two-steps: we get raw estimate of the parameter from the original data at disjoint time points and then compute the smoothed estimator from the raw estimate. The estimators are two-step local polynomial, two-step kernel, and two-step spline smoothing estimators. We derive these smoothing estimators by modeling raw estimates of the time-variant parameter from any regression or probability model, or quantile from unknown functional data and then establish a mathematical relationship. Asymptotic Bias, Variance and MSE of these estimators has been derived. Application of our methods have been demonstrated by longitudinal and cross-sectional sample data. Simulation studies under cross-sectional and longitudinal frameworks have been conducted to check the finite sample properties of our procedures. Smaller bootstrap confidence band, MSE and BIAS, and higher coverage probabilities from application and simulation show the superiority of local polynomial and spline smoothing over the kernel smoothing estimator.