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Area of Science:

  • Statistics
  • Computational Statistics

Background:

  • Non-parametric bootstrap is computationally intensive for sample moment statistics.
  • Existing implementations in R can be slow due to loop-based operations.

Purpose of the Study:

  • To develop a vectorized, computationally efficient implementation of the non-parametric bootstrap.
  • To improve the performance of bootstrapping sample moment statistics, particularly in R.

Main Methods:

  • Vectorized implementation using the multinomial sampling formulation of the non-parametric bootstrap.
  • Computation of bootstrap replications via matrix multiplications with bootstrap weights.
  • Comparison against existing R implementations and a loop-based approach.

Main Results:

  • The vectorized bootstrap demonstrated favorable performance against state-of-the-art implementations.
  • It was considerably faster for small to moderate sample sizes.
  • Slightly slower for large sample sizes due to weight matrix generation overhead.

Conclusions:

  • Vectorized bootstrap offers a significant speed advantage for bootstrapping sample moment statistics in R.
  • This method is particularly beneficial for small to moderate datasets.
  • Further optimization may be needed for very large sample sizes.