Do applied statisticians prefer more randomness or less? Bootstrap or Jackknife?

Bootstrap and Jackknife estimates, \(T_{n,B}^*\) $T_{n,B}^{\ast }$ and \(T_{n,J},\) $T_{n,J},$ respectively, of a population parameter \(\theta \) $\theta$ are both used in statistical computations; n is the sample size, B is the number of Bootstrap samples. For any \(n_0\) $n_0$ and \(B_0,\) $B_0,$ Bootstrap samples do not add new information about \(\theta \) $\theta$ being observations from the original sample and when \(B_0<\infty ,\) $B_0<\infty ,$ \(T_{n_0,B_0}^*\) $T_{n_0,B_0}^{\ast }$ includes also resampling variability, an additional source of uncertainty not affecting \(T_{n_0, J}.\) $T_{n_0,J}.$ These are neglected in theoretical papers with results for the utopian \(T_{n, \infty }^*, \) $T_{n,\infty }^{\ast },$ that do not hold for \(B<\infty .\) $B<\infty .$ The consequence is that \(T^*_{n_0, B_0}\) $T_{n_0,B_0}^{\ast }$ is expected to have larger mean squared error (MSE) than \(T_{n_0,J},\) $T_{n_0,J},$ namely \(T_{n_0,B_0}^*\) $T_{n_0,B_0}^{\ast }$ is inadmissible. The amount of inadmissibility may be very large when populations’ parameters, e.g. the variance, are unbounded and/or with big data. A palliating remedy is increasing B,  the larger the better, but the MSEs ordering remains unchanged for \(B<\infty .\) $B<\infty .$ This is confirmed theoretically when \(\theta \) $\theta$ is the mean of a population, and is observed in the estimated total MSE for linear regression coefficients. In the latter, the chance the estimated total MSE with \(T_{n,B}^*\) $T_{n,B}^{\ast }$ improves that with \(T_{n,J}\) $T_{n,J}$ decreases to 0 as B increases.