P. J. Green’s scientific contributions

... The Leverage method is one of the most important techniques available to determine the model's application scope. [89,90] In this study, the analysis of the application scope for the CMIS model was carried out using this technique, which is expressed in the form of visual analysis through William's plot. The parameter of standardized residuals (R) is used to determine the difference between the model's prediction and the actual experimental data and is expressed by the following Equation (28): [91] R j = e j ( MSE ( 1 − H jj )) 0.5 (28) where e j represents the variance between the predicted values and the experimental results for the jth data, H jj represents the Leverage of the jth data point, and the MSE parameter represents the model's mean squared error. ...

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Accurate Prediction of Hybrid Nanofluids Viscosity: A Comparison of Soft Computational Approaches, Empirical, and Theoretical Models

... When the copula is not involved in the log-likelihood, the marginal estimator derived from functional gradient descent is equivalent to kernel density estimation. Therefore we consider bandwidth selection rules from kernel density estimation, such as Silverman's Rule of Thumb (Silverman 2018) and Scott's Rule (Scott 2015). We also consider the sample standard deviations of the marginal variables as a bandwidth selection rule. ...

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Unbalanced Longitudinal Data Clustering with a Copula Kernel Mixture Model

... Wahba [3], Green and Silverman [4] and Schimek [5] considered smoothing splines approach, Robinson [6] and Speckman [7] discussed kernel smoothing, Ruppert et al. [8] and Liang [9] adopted penalized spline, and Aydın and Yilmaz [10] generalized the conventional approximation to censored partially linear regression model using different smoothing methods such as smoothing spline, kernel smoothing, and penalized spline, to name the most important. Here we follow the smoothing splines approach of Green and Silverman [4] based on the study of Green et al. [11]. ...

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Rational (Padé) approximation for estimating the components of the partially-linear regression model