scholarly journals Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains

1978 ◽  
Vol 28 (4) ◽  
pp. 147-167 ◽  
Author(s):  
Jang-Mei G. Wu
Keyword(s):  
Kernel Functions ◽  
Lipschitz Domains ◽  
Boundary Harnack Principle ◽  
Fatou Theorem ◽  
Relative Fatou Theorem

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

The Spinning Quality Control Management Based on Decision Making by Data Mining Techniques

2018 ◽  
Vol 7 (1) ◽  
pp. 72
Author(s):  
Khalid AA Abakar ◽  
Chongwen Yu
Keyword(s):  
Data Mining ◽  
Kernel Functions ◽  
Support Vector ◽  
Ann Model ◽  
Data Mining Techniques ◽  
Yarn Quality ◽  
Yarn Properties ◽  
Svm Model ◽  
Rbf Kernel

This work demonstrated the possibility of using the data mining techniques such as artificial neural networks (ANN) and support vector machine (SVM) based model to predict the quality of the spinning yarn parameters. Three different kernel functions were used as SVM kernel functions which are Polynomial and Radial Basis Function (RBF) and Pearson VII Function-based Universal Kernel (PUK) and ANN model were used as data mining techniques to predict yarn properties. In this paper, it was found that the SVM model based on Person VII kernel function (PUK) have the same performance in prediction of spinning yarn quality in comparison with SVM based RBF kernel. The comparison with the ANN model showed that the two SVM models give a better prediction performance than an ANN model.

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