Assessing Variability of Complex Descriptive Statistics in Monte Carlo Studies using Resampling Methods.

Area of Science:

• Statistical Methods
• Computational Statistics
• Data Analysis

Background:

• Standard errors are crucial for summarizing Monte Carlo simulation results.
• Calculating standard errors for complex statistics like medians or variances can be challenging.
• The Delta Method, while theoretically applicable, often presents practical barriers.

Purpose of the Study:

• To demonstrate the simplicity of using resampling methods for standard error calculation.
• To provide accessible methods for obtaining standard errors of complex Monte Carlo summaries.
• To highlight alternatives to the Delta Method for standard error estimation.

Main Methods:

• Application of the jackknife resampling technique.
• Implementation of the bootstrap resampling method.
• Comparison of resampling methods with the Delta Method for complex statistics.

Main Results:

• Jackknife and bootstrap methods provide straightforward computation of standard errors.
• These methods are effective even for complex summary statistics (e.g., medians, variances, skewness).
• Resampling approaches overcome the practical difficulties associated with the Delta Method.

Conclusions:

• The jackknife and bootstrap are practical and simple tools for computing standard errors in Monte Carlo studies.
• These methods enhance the reporting of statistical accuracy for a wider range of summary measures.
• Researchers can readily implement these techniques to improve the rigor of their simulation studies.