Is nonparametric bootstrap an appropriate technique for estimating variance of the sample median?

Abstract

The main objective of this study is to compare two different bootstrap algorithms for estimating the variance of sample median when the underlying distribution is symmetric, right or left skewed. Nonparametric bootstrap method and the formulated estimation approach of bootstrap method proposed by Ghosh et al., were compared at different sample sizes using Monte Carlo simulation technique. Simulation results showed that nonparametric bootstrap method has better efficiency for symmetric or right skewed distributions when the sample size was small. However, it had lower efficiency for left skewed distributions. For large sample sizes, both estimation methods gave similar variance estimates with lower bias.

Subject Classification: (2010):

• 62F40
• 62G05

Keywords:

• Non-parametric bootstrap
• Estimation
• Variance
• Sample median