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.

Highlights

  • This work deals with the well known problem of data-driven choice of smoothing parameters in nonparametric density and hazard rate estimation

  • Bootstrap methods are used for bandwidth selection in: (1) nonparametric kernel density estimation with dependent data, and (2) nonparametric kernel hazard rate estimation

  • Four new bandwidth parameter selectors are proposed based on closed bootstrap expressions of the MISE of the kernel density estimator and two approximations of the kernel hazard rate estimation

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Summary

Introduction

This work deals with the well known problem of data-driven choice of smoothing parameters in nonparametric density and hazard rate estimation (see [1,2,3,4]). Our aim is to propose new bootstrap procedures for nonparametric density estimation considering dependent data. Hazard rate estimation is considered and two bootstrap bandwidth selectors based on some approximation of the kernel hazard rate estimator are proposed

Nonparametric Density Estimation
Nonparametric Hazard Rate Estimation
Simulation Results
Discussion

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