Resampling methods with multiply imputed data.

Area of Science:

• Statistics
• Data Science
• Computational Statistics

Background:

• Resampling techniques (jackknife, bootstrap) are vital for uncertainty estimation.
• Missing data are common and often handled by imputation, including multiple imputation.
• Combining resampling with stochastic imputation presents unique theoretical challenges.

Purpose of the Study:

• To derive the theory for using jackknife and bootstrap with stochastic imputation.
• To provide guidance on the correct implementation of these methods.
• To address the interplay between replicate groups and imputed datasets.

Main Methods:

• Theoretical derivation of resampling rules for stochastic imputation.
• Analysis of jackknife and bootstrap approaches under multiple imputation.
• Discussion of bias-adjusted jackknife and bootstrap methods.
• Simulation study to validate theoretical findings.

Main Results:

• Imputations must be generated independently within each replicate group for both jackknife and bootstrap.
• Jackknife requires significantly more imputed datasets than replicate groups.
• Bootstrap does not have the same stringent requirement for the number of imputed datasets relative to replicate groups.
• Bias-adjusted methods may reduce the need for numerous imputed datasets.

Conclusions:

• Proper application of resampling with stochastic imputation requires careful consideration of imputation generation and dataset numbers.
• The theoretical framework clarifies optimal strategies for uncertainty estimation in incomplete datasets.
• Findings offer practical guidance for researchers using these advanced statistical methods.