A Comparison Study of Parametric and Semiparametric Bootstrapping in Deterministic Simulation

In deterministic simulation model, kriging predictor is an exact interpolation which ignores the randomness of errors in sampled Input/Output (I/O) data. Inserting kriging model parameter estimators based on sampled I/O data into kriging predictors produced underestimated or biased variance estimator. This paper is a comparative study for two methods of unbiased variance generic estimators of kriging prediction, which were obtained by inserting randomness of sampled output into deterministic simulation model. This randomness was generated by semiparametric bootstrapping and parametric bootstrapping. Comparison of the performance of both bootstrapping would be measured on a small number of unsampled input points (untried points) by considering: (i) estimation values of both generic estimators of kriging variance (bootstrap kriging variance), (ii) coverage probability and length of confidence interval of Kriging prediction of both boostrappings. Simulation with bootstrap sample size B = 10000 and various data dimension, showed smaller estimation of semiparametric bootstrap kriging variance than parameteric. Coverage probability of semiparametric and parametric bootstrap percentiles were exactly the same as nominal coverages, while standard normal coverage based on parametric bootstrapping was very different from nominal coverage. Length of estimation of confidence interval based on semiparametric bootstrapped was shorter than parametric. Generally, the performance of semiparametric bootstrapping gave was better than parametric bootstrapping.