SIFAT ASIMTOTIK VARIANSI KRIGING BOOTSTRAPPING SEMIPARAMETRIK DALAM SIMULASI DETERMINISTIK; ASYMPTOTIC PROPERTY OF SEMIPARAMETRIC BOOTSTRAPPING KRIGING VARIANCE IN DETERMINISTIC SIMULATION

Simamora, Elmanani, Subanar

2016 | Tesis | FMIPA

In the deterministic simulation model, kriging predictor is an exact interpolation that ignore the randomness of output data on the observed input data. Plungging-in kriging model parameter estimation based on the observed I/O data provides plug-in kriging prediction EBLUP but the variance estimation is being underestimated or biased. Hertog et al. (2006) provide a correction by generating the uncertainties of output data in the observed input data using parametric bootstrapping. The generic estimator of the kriging variance (parametric bootstrapping kriging variance) gives poor results, because the estimation is very far from the kriging variance EBLUP (plug-in kriging variance). This research proposes a new procedure in deterministic simulation to determine the generic estimator of kriging variance BLUP using semiparametric bootstrapping. Simulation shows the estimation of the bootstrapping semiparametric kriging variance is always greater than the plug-in kriging variance and decrease in the estimation of the plug-ins kriging variance and bootstrapping semiparametric kriging variance tends to zero. Estimates of sampling distribution gives mixed results on the Gaussian distribution. For a onedimensional input data, the estimation of sampling distribution provides the estimation of the distribution that is far from a Gaussian distribution. For twodimensional input data, the estimation of sampling distribution provides the estimation of sampling distribution approach the Gaussian distribution and a three-dimensional input data showed almost sure the Gaussian distribution. This research also conducted analytic study to prove that plug-in kriging variance and semiparametric bootstrapping kriging variance is convergent with probability one to zero. As a result, the asymptotic properties of plug-in kriging variance and semiparametric bootstrapping kriging variance is strong consistency to zero.

Kata Kunci : Kriging, Variance, Bootstrapping, Asymptotic, Simulation