Kok, S2012-08-022012-08-022012-07Kok, S. The asymptotic behaviour of the maximum likelihood function of Kriging approximations using the Gaussian correlation function. EngOpt 2012 - International Conference on Engineering Optimization, Rio de Janeiro, Brazil, 1-5 July 2012978-85-7650-344-6http://www.engopt.org/paper/342.pdfhttp://hdl.handle.net/10204/6033EngOpt 2012 - International Conference on Engineering Optimization, Rio de Janeiro, Brazil, 1-5 July 2012This study reports on the asymptotic behavior of the maximum likelihood function, encountered when constructing Kriging approximations using the Gaussian correlation function. Of specific interest is a maximum likelihood function that decreases continuously as the correlation function hyper-parameters approach zero. Since the global minimizer of the maximum likelihood function is an asymptote in this case, it is unclear if maximum likelihood estimation (MLE) remains valid. Numerical ill-conditioning of the correlation matrix also occurs in this case. Analytical and numerical examples are presented that demonstrates the validity of MLE, provided that arbitrary precision arithmetic is used. A recent result that claims the MLE function always approaches infinity as the hyper-parameters approach zero is also disproved.enKrigingMaximum Likelihood EstimationGaussian correlation functionIll-conditioningConference PresentationKok, S. (2012). The asymptotic behaviour of the maximum likelihood function of Kriging approximations using the Gaussian correlation function. http://hdl.handle.net/10204/6033Kok, S. "The asymptotic behaviour of the maximum likelihood function of Kriging approximations using the Gaussian correlation function." (2012): http://hdl.handle.net/10204/6033Kok S, The asymptotic behaviour of the maximum likelihood function of Kriging approximations using the Gaussian correlation function; 2012. http://hdl.handle.net/10204/6033 .TY - Conference Presentation AU - Kok, S AB - This study reports on the asymptotic behavior of the maximum likelihood function, encountered when constructing Kriging approximations using the Gaussian correlation function. Of specific interest is a maximum likelihood function that decreases continuously as the correlation function hyper-parameters approach zero. Since the global minimizer of the maximum likelihood function is an asymptote in this case, it is unclear if maximum likelihood estimation (MLE) remains valid. Numerical ill-conditioning of the correlation matrix also occurs in this case. Analytical and numerical examples are presented that demonstrates the validity of MLE, provided that arbitrary precision arithmetic is used. A recent result that claims the MLE function always approaches infinity as the hyper-parameters approach zero is also disproved. DA - 2012-07 DB - ResearchSpace DP - CSIR KW - Kriging KW - Maximum Likelihood Estimation KW - Gaussian correlation function KW - Ill-conditioning LK - https://researchspace.csir.co.za PY - 2012 SM - 978-85-7650-344-6 T1 - The asymptotic behaviour of the maximum likelihood function of Kriging approximations using the Gaussian correlation function TI - The asymptotic behaviour of the maximum likelihood function of Kriging approximations using the Gaussian correlation function UR - http://hdl.handle.net/10204/6033 ER -