Metamodeling complex systems using linear and nonlinear regression methods

Kartal, Elçin
Metamodeling is a very popular approach for the approximation of complex systems. Metamodeling techniques can be categorized according to the type of regression method employed as linear and nonlinear models. The Response Surface Methodology (RSM) is an example of linear regression. In classical RSM metamodels, parameters are estimated using the Least Squares (LS) Method. Robust regression techniques, such as Least Absolute Deviation (LAD) and M-regression, are also considered in this study due to the outliers existing in data sets. Artificial Neural Networks (ANN) and Multivariate Adaptive Regression Splines (MARS) are examples for non-linear regression technique. In this thesis these two nonlinear metamodeling techniques are constructed and their performances are compared with the performances of linear models.


Autoregressive models with short-tailed symmetric distributions
Akkaya, Ayşen (Informa UK Limited, 2008-01-01)
Symmetric short-tailed distributions do indeed occur in practice but have not received much attention particularly in the context of autoregression. We consider a family of such distributions and derive the modified maximum likelihood estimators of the parameters. We show that the estimators are efficient and robust. We develop hypothesis-testing procedures.
Multiple linear regression model with stochastic design variables
İslam, Muhammed Qamarul (Informa UK Limited, 2010-01-01)
In a simple multiple linear regression model, the design variables have traditionally been assumed to be non-stochastic. In numerous real-life situations, however, they are stochastic and non-normal. Estimators of parameters applicable to such situations are developed. It is shown that these estimators are efficient and robust. A real-life example is given.
A computational approach to nonparametric regression: bootstrapping cmars method
Yazıcı, Ceyda; Batmaz, İnci; Department of Statistics (2011)
Bootstrapping is a resampling technique which treats the original data set as a population and draws samples from it with replacement. This technique is widely used, especially, in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a special case of nonparametric regression, Conic Multivariate Adaptive Regression Splines (CMARS). Here, the CMARS method, which uses conic quadr...
Mutual information model selection algorithm for time series
Akca, Elif; Yozgatlıgil, Ceylan (Informa UK Limited, 2020-09-01)
Time series model selection has been widely studied in recent years. It is of importance to select the best model among candidate models proposed for a series in terms of explaining the procedure that governs the series and providing the most accurate forecast for the future observations. In this study, it is aimed to create an algorithm for order selection in Box-Jenkins models that combines penalized natural logarithm of mutual information among the original series and predictions coming from each candida...
Linear contrasts in experimental design with non-identical error distributions
Senoglu, B; Tiku, ML (Wiley, 2002-01-01)
Estimation of linear contrasts in experimental design, and testing their assumed values, is considered when the error distributions from block to block are not necessarily identical. The normal-theory solutions are shown to have low efficiencies as compared to the solutions presented here.
Citation Formats
E. Kartal, “Metamodeling complex systems using linear and nonlinear regression methods,” M.S. - Master of Science, Middle East Technical University, 2007.