MonteCarloJackknife.jl: Fast and Scalable Monte Carlo Approximation of Delete-d Jackknife Estimators in Julia

This paper introduces MonteCarloJackknife.jl, an open-source Julia package that implements Monte Carlo approximation of delete-d jackknife estimators. Rather than exhaustively enumerating all deletion subsets, the package randomly samples a user-specified number of subsets, computes the parameter of interest on these subsets and combines their values. This reduces the computational complexity from combinatorial in the number of possible subsets to linear in the number of Monte Carlo samples while retaining the flexibility of the deleted jackknife framework. The package accepts arbitrary user-defined Julia functions, supports both scalar and vector-valued estimators, provides optional multithreaded execution, and returns Monte Carlo estimates together with estimated standard errors and the corresponding jackknife replicates. The generic implementation makes the package applicable to a wide range of statistical procedures and modern machine learning models. Several examples demonstrate that accurate approximations can be obtained using only a small fraction of all possible delete-d subsets, making delete-d jackknife practical for problems that are computationally intractable under exhaustive enumeration.