Comparative Analysis on Kernel Based Probability Density Estimation

2014 ◽  
Vol 543-547 ◽  
pp. 1655-1658
Author(s):  
Xiang Ran Du ◽  
Hai Tao Liu ◽  
Min Zhang
Keyword(s):  
Probability Density ◽  
Density Estimation ◽  
Mean Squared Error ◽  
Estimation Error ◽  
Probability Density Estimation ◽  
Estimation Errors ◽  
Squared Error ◽  
Window Method ◽  
Selection Of ◽  
Experimental Comparisons

In this paper, we compare the estimation performances of 7 different kernels (i.e., Uniform, Triangular, Epanechnikov, Biweight, Triweight, Cosine and Gaussian) when using them to conduct the probability density estimation with Parzen window method. We firstly analyze the efficiencies of these 7 kernels and then compare their estimation errors measured by mean squared error (MSE). The theoretical analysis and the experimental comparisons show that the mostly-used Gaussian kernel is not the best choice for the probability density estimation, of which the efficiency is low and estimation error is high. The derived conclusions give some guidelines for the selection of kernel in the practical application of probability density estimation.

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.

On the Use of a Modified Intersection of Confidence Intervals (MICIH) Kernel Density Estimation Approach

2021 ◽  
Vol 8 (4) ◽  
pp. 309-332
Author(s):  
Efosa Michael Ogbeide ◽  
Joseph Erunmwosa Osemwenkhae
Keyword(s):  
Confidence Intervals ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Mean Squared Error ◽  
Kernel Density ◽  
Window Size ◽  
National Bureau ◽  
Squared Error ◽  
Data Density ◽  
Adaptive Kernel

Density estimation is an important aspect of statistics. Statistical inference often requires the knowledge of observed data density. A common method of density estimation is the kernel density estimation (KDE). It is a nonparametric estimation approach which requires a kernel function and a window size (smoothing parameter H). It aids density estimation and pattern recognition. So, this work focuses on the use of a modified intersection of confidence intervals (MICIH) approach in estimating density. The Nigerian crime rate data reported to the Police as reported by the National Bureau of Statistics was used to demonstrate this new approach. This approach in the multivariate kernel density estimation is based on the data. The main way to improve density estimation is to obtain a reduced mean squared error (MSE), the errors for this approach was evaluated. Some improvements were seen. The aim is to achieve adaptive kernel density estimation. This was achieved under a sufficiently smoothing technique. This adaptive approach was based on the bandwidths selection. The quality of the estimates obtained of the MICIH approach when applied, showed some improvements over the existing methods. The MICIH approach has reduced mean squared error and relative faster rate of convergence compared to some other approaches. The approach of MICIH has reduced points of discontinuities in the graphical densities the datasets. This will help to correct points of discontinuities and display adaptive density. Keywords: approach, bandwidth, estimate, error, kernel density

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