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A Practical Solution to the Small Sample Size Bias and Uncertainty Problems of Model Selection Criteria in Two-Input Process Multiple Response Surface Methodology Datasets

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Open Journal of Statistics 2019年第1期9卷 109-142页

作者： Domingo Pavolo delson chikobvu The University of the Free State Bloemfontein South Africa

Multiple response surface methodology (MRSM) most often involves the analysis of small sample size datasets which have associated inherent statistical modeling problems. Firstly, classical model selection criteria in use are very inefficient with small sample size datasets. Secondly, classical model selection criteria have an acknowledged selection uncertainty problem. Finally, there is a credibility problem associated with modeling small sample sizes of the order of most MRSM datasets. This work focuses on determination of a solution to these identified problems. The small sample model selection uncertainty problem is analysed using sixteen model selection criteria and a typical two-input MRSM dataset. Selection of candidate models, for the responses in consideration, is done based on response surface conformity to expectation to deliberately avoid selection of models using the problematic classical model selection criteria. A set of permutations of combinations of response models with conforming response surfaces is determined. Each combination is optimised and results are obtained using overlaying of data matrices. The permutation of results is then averaged to obtain credible results. Thus, a transparent multiple model approach is used to obtain the solution which gives some credibility to the small sample size results of the typical MRSM dataset. The conclusion is that, for a two-input process MRSM problem, conformity of response surfaces can be effectively used to select candidate models and thus the use of the problematic model selection criteria is avoidable.

关键词： Multiple Response Surface Methodology All Possible Regressions Model Selection Criteria Data Matrices

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Tail Quantile Estimation of Heteroskedastic Intraday Increases in Peak Electricity Demand

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Open Journal of Statistics 2012年第4期2卷 435-442页

作者： Caston Sigauke Andréhette Verster delson chikobvu Department of Mathematical Statistics and Actuarial Science University of the Free State South Africa Department of Statistics and Operations Research University of Limpopo South Africa

Modelling of intraday increases in peak electricity demand using an autoregressive moving average-exponential generalized autoregressive conditional heteroskedastic-generalized single Pareto (ARMA-EGARCH-GSP) approach is discussed in this paper. The developed model is then used for extreme tail quantile estimation using daily peak electricity demand data from South Africa for the period, years 2000 to 2011. The advantage of this modelling approach lies in its ability to capture conditional heteroskedasticity in the data through the EGARCH framework, while at the same time estimating the extreme tail quantiles through the GSP modelling framework. Empirical results show that the ARMA-EGARCH-GSP model produces more accurate estimates of extreme tails than a pure ARMA-EGARCH model.

关键词： Conditional Extreme Value Theory Daily Electricity Peak Demand Volatility Tail Quantiles

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