• Communications for Statistical Applications and Methods
• /
• v.31 no.3
• /
• pp.337-347
• /
• 2024

Kernel density estimation is a prevalent technique employed for nonparametric density estimation, enabling direct estimation from the data itself. This estimation involves two crucial elements: selection of the kernel function and the determination of the appropriate bandwidth. The selection of the bandwidth plays an important role in kernel density estimation, which has been developed over the past decade. A range of methods is available for selecting the bandwidth, including the plug-in bandwidth. In this article, the proposed plug-in bandwidth is introduced, which leverages shifted Chebyshev series-based approximation to determine the optimal bandwidth. Through a simulation study, the performance of the suggested bandwidth is analyzed to reveal its favorable performance across a wide range of distributions and sample sizes compared to alternative bandwidths. The proposed bandwidth is also applied for kernel density estimation on real dataset. The outcomes obtained from the proposed bandwidth indicate a favorable selection. Hence, this article serves as motivation to explore additional plug-in bandwidths that rely on function approximations utilizing alternative series expansions.

• ETRI Journal
• /
• v.15 no.2
• /
• pp.35-51
• /
• 1993

This paper presents function approximation based on nonparametric estimation. As an estimation model of function approximation, a three layered network composed of input, hidden and output layers is considered. The input and output layers have linear activation units while the hidden layer has nonlinear activation units or kernel functions which have the characteristics of bounds and locality. Using this type of network, a many-to-one function is synthesized over the domain of the input space by a number of kernel functions. In this network, we have to estimate the necessary number of kernel functions as well as the parameters associated with kernel functions. For this purpose, a new method of parameter estimation in which linear learning rule is applied between hidden and output layers while nonlinear (piecewise-linear) learning rule is applied between input and hidden layers, is considered. The linear learning rule updates the output weights between hidden and output layers based on the Linear Minimization of Mean Square Error (LMMSE) sense in the space of kernel functions while the nonlinear learning rule updates the parameters of kernel functions based on the gradient of the actual output of network with respect to the parameters (especially, the shape) of kernel functions. This approach of parameter adaptation provides near optimal values of the parameters associated with kernel functions in the sense of minimizing mean square error. As a result, the suggested nonparametric estimation provides an efficient way of function approximation from the view point of the number of kernel functions as well as learning speed.

• Journal of IKEEE
• /
• v.21 no.1
• /
• pp.46-65
• /
• 2017

This paper proposes a fast patch-based de-blurring algorithm including kernel estimation based on the angle between the edge and the blur direction. For de-blurring, image patches from the most informative edges in the blurry image are used to estimate a kernel with low computational cost. Moreover, the kernels of each patch are estimated based on the correlation between the edge direction and the blur direction. This makes the final kernel more reliable and creates an accurate latent image from the blurry image. The combination of directionally oriented kernel estimation and patch-based de-blurring is faster and more accurate than existing state-of-the art methods. Experimental results using various test images show that the proposed method achieves its objectives: speed and accuracy.

• Communications for Statistical Applications and Methods
• /
• v.15 no.6
• /
• pp.939-946
• /
• 2008

In this paper the support vector method is presented for the probability density function estimation when the sample observations are contaminated with random noise. The performance of the procedure is compared to kernel density estimates by the simulation study.

• Communications for Statistical Applications and Methods
• /
• v.2 no.2
• /
• pp.227-230
• /
• 1995

In this paper, we discuss simple ways of implementing non-basic kernel density estimators which typically ceed extra pilot estimation. The methods utilize order statistics at the pilot estimation stages. We focus mainly on bariable lacation and scale kernel density estimator (Jones, Hu and McKay, 1994), but the same idea can be applied to other methods too.

• Journal of the Korean Statistical Society
• /
• v.20 no.1
• /
• pp.1-28
• /
• 1991

Considerable progress on the problem of data-driven bandwidth selection in kernel density estimation has been made recently. The goal of this paper is to provide an introduction to the methods currently available, with discussion at both a practical and a nontechnical theoretical level. The main setting considered here is global bandwidth kernel estimation, but some recent results on variable bandwidth kernel estimation are also included.

• Journal of the Korean Data and Information Science Society
• /
• v.3 no.1
• /
• pp.17-24
• /
• 1992

The problem of estimating symmetric probability density with high kurtosis is considered. Such densities are often estimated poorly by a global bandwidth kernel estimation since good estimation of the peak of the distribution leads to unsatisfactory estimation of the tails and vice versa. In this paper, we propose a transformation technique before using a global bandwidth kernel estimator. Performance of density estimator based on proposed transformation is investigated through simulation study. It is observed that our method offers a substantial improvement for the densities with high kurtosis. However, its performance is a little worse than that of ordinary kernel estimator in the situation where the kurtosis is not high.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.22 no.5
• /
• pp.561-566
• /
• 2021

The optimum kernel size for error-distribution estimation with given error samples cannot be used in the weight adjustment of minimum Euclidean distance between error distributions (MED) algorithms. In this paper, a new adaptive kernel estimation method for convergence enhancement of MED algorithms is proposed. The proposed method uses the average rate of change in error power with respect to a small interval of the kernel width for weight adjustment of the MED learning algorithm. The proposed kernel adjustment method is applied to experiments in communication channel compensation, and performance improvement is demonstrated. Unlike the conventional method yielding a very small kernel calculated through optimum estimation of error distribution, the proposed method converges to an appropriate kernel size for weight adjustment of the MED algorithm. The experimental results confirm that the proposed kernel estimation method for MED can be considered a method that can solve the sensitivity problem from choosing an appropriate kernel size for the MED algorithm.

• Communications for Statistical Applications and Methods
• /
• v.10 no.2
• /
• pp.607-617
• /
• 2003

This paper offers a practical comparison of efficiency between local likelihood approach and conventional kernel approach in density estimation. The local likelihood estimation procedure maximizes a kernel smoothed log-likelihood function with respect to a polynomial approximation of the log likelihood function. We use two types of data driven bandwidths for each method and compare the mean integrated squares for several densities. Numerical results reveal that local log-linear approach with simple plug-in bandwidth shows better performance comparing to the standard kernel approach in heavy tailed distribution. For normal mixture density cases, standard kernel estimator with the bandwidth in Sheather and Jones(1991) dominates the others in moderately large sample size.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2014.05a
• /
• pp.86-88
• /
• 2014

Naive Bayes (NB) assumption has some harmful effects in classification to the real world data. To relax this assumption, we now propose approach called Naive Bayes Mutual Information Attribute Weighting with Smooth Kernel Density Estimation (NBMIKDE) that combine the smooth kernel for attribute and attribute weighting method based on mutual information measure.