Autocorrelation problem causes unduly effects on the variance of Ordinary Least Squares (OLS) estimates. Hence, it is very essential to detect the autocorrelation problem so that appropriate remedial measures can be taken. The Breusch-Godfrey (BG) test is the most popular and commonly used test for the detection of autocorrelation. Since this test is based on the OLS estimates, which are not robust, it is easily affected by outliers. In this paper, we propose a robust Breusch-Godfrey (MBG) test which is not easily affected by outliers. The results of the study indicate that the MBG test is more powerful than the BG test in the detection of autocorrelation problem.
Extreme Value Theory (EVT) is a statistical field whose main focus is to investigate extreme phenomena. In EVT, Fréchet distribution is one of the extreme value distributions and it is used to model extreme events. The degree of fit between the model and the observed values was measured by Goodness-of-fit (GOF) test. Several types of GOF tests were also compared. The tests involved were Anderson-Darling (AD), Cramer-von Mises (CVM), Zhang Anderson Darling (ZAD), Zhang Cramer von-Mises (ZCVM) and Ln. The values of parameters μ, σ and ξ were estimated by Maximum Likelihood. The critical values were developed by Monte-Carlo simulation. In power study, the reliability of critical values was determined. Besides, it is of interest to identify which GOF test is superior to the other tests for Fréchet distribution. Thus, the comparisons of rejection rates were observed at different significance levels, as well as different sample sizes, based on several alternative distributions. Overall, given by Maximum Likelihood Estimation of Fréchet distribution, the ZAD and ZCVM tests are the most powerful tests for smaller sample size (ZAD for significance levels 0.05 and 0.1, ZCVM for significance level 0.01) as compared to AD, which is more powerful for larger sample size.
The extraction of relevant wavelengths from a large dataset of Near Infrared Spectroscopy (NIRS) is a significant challenge in vibrational spectroscopy research. Nonetheless, this process allows the improvement in the chemical interpretability by emphasizing the chemical entities related to the chemical parameters of samples. With the complexity in the dataset, it may be possible that irrelevant wavelengths are still included in the multivariate calibration. This yields the computational process to become unnecessary complex and decreases the accuracy and robustness of the model. In multivariate analysis, Partial Least Square Regression (PLSR) is a method commonly used to build a predictive model from NIR spectral data. However, in the PLSR method and common commercial chemometrics software, there is no standard wavelength selection procedure applied to screen the irrelevant wavelengths. In this study, a new robust wavelength selection procedure called the modified VIP-MCUVE (mod-VIP-MCUVE) using Filter-Wrapper method and input scaling strategy is introduced. The proposed method combines the modified Variable Importance in Projection (VIP) and modified Monte Carlo Uninformative Variable Elimination (MCUVE) to calculate the scale matrix of the input variable. The modified VIP uses the orthogonal components of Partial Least Square (PLS) in investigating the informative variable in the model by applying the amount of variation both in X and y{SSX,SSY}, simultaneously. The modified MCUVE uses a robust reliability coefficient and a robust tolerance interval in the selection procedure. To evaluate the superiority of the proposed method, the classical VIP, MCUVE, and autoscaling procedure in classical PLSR were also included in the evaluation. Using artificial data with Monte Carlo simulation and NIR spectral data of oil palm (Elaeis guineensis Jacq.) fruit mesocarp, the study shows that the proposed method offers advantages to improve model interpretability, to be computationally extensive, and to produce better model accuracy.
In practice, the collected spectra are very often composes of complex overtone and many overlapping peaks which may lead to misinterpretation because of its significant nonlinear characteristics. Using linear solution might not be appropriate. In addition, with a high-dimension of dataset due to large number of observations and data points the classical multiple regressions will neglect to fit. These complexities commonly will impact to multicollinearity problem, furthermore the risk of contamination of multiple outliers and high leverage points also increases. To address these problems, a new method called Kernel Partial Diagnostic Robust Potential (KPDRGP) is introduced. The method allows the nonlinear solution which maps nonlinearly the original input
X
matrix into higher dimensional feature mapping with corresponds to the Reproducing Kernel Hilbert Spaces (RKHS). In dimensional reduction, the method replaces the dot products calculation of elements in the mapped data to a nonlinear function in the original input space. To prevent the contamination of the multiple outlier and high leverage points the robust procedure using Diagnostic Robust Generalized Potentials (DRGP) algorithm was used. The results verified that using the simulation and real data, the proposed KPDRGP method was superior to the methods in the class of non-kernel and some other robust methods with kernel solution.