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Nonlinear filtering
Published in Alexander D. Poularikas, ®, 2018
Definition 8.6 The L-estimators are of the form: () L-estimatorθ^=∑i=1Naix(i),ais=constants
Prognostic Performance Metrics
Published in Ashok N. Srivastava, Jiawei Han, Machine Learning and Knowledge Discovery for Engineering Systems Health Management, 2016
Kai Goebel, Abhinav Saxena, Sankalita Saha, Bhaskar Saha, Jose Celaya
A prognostic system models a stochastic process, and hence, the behavior observed from a particular run (single realization of the stochastic process) does not represent the complete behavior of the predicted trajectories. Assuming that all measures practically possible for uncertainty reduction have been taken during the algorithm development phase, such observations should be treated only as isolated realization of the process. A level of confidence or probability of occurrence should be attached to such predictions. Otherwise, multiple trajectories should be aggregated from several runs to achieve statistical significance and more sophisticated stochastic analyses may be carried out. Another aspect dealing with uncertainties is related to prognostic algorithm output. Different algorithms represent uncertainties in different ways. Some specify parametric distribution and others as nonparametric ones. Furthermore, some result in a closed form analytical equation for these distributions and others only result in discretized histograms. It is very important to carefully treat these distributions and not lose critical information by approximating these by known simpler forms such as normal distribution or by computing their statistical moments [4,37]. A common practice has been to compute mean and variance for all types of distributions whereas they may not be very meaningful for nonnormal distributions. Use of more robust estimators such as median, L-estimator, or M-estimator for expressing central tendency and IQR, MAD, or MdAD for expressing the spread is suggested [41].
Modeling energy content of municipal solid waste based on proximate analysis: R-k class estimator approach
Published in Cogent Engineering, 2022
Rotimi Adedayo Ibikunle, Adewale Folaranmi Lukman, Isaac Femi Titiladunayo, Abdul-Rahaman Haadi
Most work on the modeling of the HHV of MSW earlier mentioned adopted the ordinary least squares estimator. Literature has shown that the predictor variables might be correlated, which gives rise to multicollinearity. The OLS estimator suffers a setback when there is multicollinearity (Lukman & Ayinde, 2017; Lukman et al., 2019a, 2019b). The consequences of multicollinearity to the OLS estimator include large variance, insignificant t-test, wider confidence interval, wrong regression coefficients, and others (Ayinde et al., 2018; Dawoud & Kibria, 2020; Lukman & Ayinde, 2017; Qasim et al., 2019). Multicollinearity can be tested using the following methods: variance inflation factor, condition number, condition index, eigenvalues, and others (Aslam & Ahmad, 2020; Ibikunle et al., 2020b, 2020a). Different estimators have been proposed to estimate the parameter when there is multicollinearity. These include the principal component regression estimator (PCRE) by Massy (1965), the ridge estimator by Hoerl and Kennard (1970), the Liu estimator by Liu (1993), the modified Liu estimator by Lukman et al. (2020a), and the K-L estimator by Kibria and Lukman (2020).
Analysis-of-Marginal-Tail-Means (ATM): A Robust Method for Discrete Black-Box Optimization
Published in Technometrics, 2019
The conditional tail mean (6) can be also be viewed more generally as an L-estimator (Huber 1974)—a linear combination of order statistics. In robust statistics, L-estimators have been widely used for robust estimation. We show next how the same tail means, when used as marginal statistics, enable robust optimization as well.
Modeling and robust prediction of high heating values of municipal solid waste based on ultimate analysis
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Rotimi A. Ibikunle, Adewale F. Lukman, Isaac F. Titiladunayo, Emmanuel A. Akeju, Samuel O. Dahunsi
where is the ith eigenvalue of matrix. The robust K-L estimator is defined in the following equation as :