Computationally Efficient Bootstrap Expressions for Bandwidth Selection in Nonparametric Curve Estimation

Abstract

Bootstrap methods are used for bandwidth selection in: (1) nonparametric kernel density estimation with dependent data (smoothed stationary bootstrap and smoothed moving blocks bootstrap), and (2) nonparametric kernel hazard rate estimation (smoothed bootstrap). In these contexts, four new bandwidth parameter selectors are proposed based on closed bootstrap expressions of the MISE of the kernel density estimator (case 1) and two approximations of the kernel hazard rate estimation (case 2). These expressions turn out to be very useful since Monte Carlo approximation is no longer needed. Finally, these smoothing parameter selectors are empirically compared with the already existing ones via a simulation study.

Keywords

• hazard rate
• Kernel Method
• Mean integrated squared error
• moving blocks bootstrap
• Smooth Bootstrap
• smoothing parameter
• stationary bootstrap
• Stationary Processes