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

• Journal of the Korean Statistical Society
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• v.20 no.1
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• pp.1-28
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• 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 Statistical Society
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• v.17 no.1
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• pp.1-8
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• 1988

Kernel estimates of an unknown regression function are studied. Bandwidth selection rule minimizing integrated absolute error loss function is considered. Under some reasonable assumptions, it is shown that the optimal bandwidth is unique and can be computed by using bisection algorithm. Adaptive bandwidth selection rule is proposed.

• Journal of the Korean Data and Information Science Society
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• v.5 no.1
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• pp.11-20
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• 1994

In recent years, nonparametric kernel estimation of regresion function are abundant and widely applicable to many areas of statistics. Most of modern researches concerned with the fixed global bandwidth selection which can be used in the estimation of regression function with all the same value for all x. In this paper, we propose a method for selecting locally varing bandwidth based on bootstrap method in kernel estimation of fixed design regression. Performance of proposed bandwidth selection method for finite sample case is conducted via Monte Carlo simulation study.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.453-463
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• 1997

Nonparametric kernel regression has recently gained widespread acceptance as an attractive method for the nonparametric estimation of the mean function from noisy regression data. Also, the practical implementation of kernel method is enhanced by the availability of reliable rule for automatic selection of the bandwidth. In this article, we propose a method for automatic selection of the bandwidth that minimizes the asymptotic mean square error. Then, the estimated bandwidth by the proposed method is compared with the theoretical optimal bandwidth and a bandwidth by plug-in method. Simulation study is performed and shows satisfactory behavior of the proposed method.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.361-368
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• 1993

In recent years, kernel type estimates are abundant. In this paper, we propose a bandwidth selection method for kernel regression of fixed design based on bootstrap procedure. Mathematical properties of proposed bootstrap-based bandwidth selection method are discussed. Performance of the proposed method for small sample case is compared with that of cross-validation method via a simulation study.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.1-5
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• 2002

We consider the problem of optimal bandwidth choice for nonparametric classification, based on kernel density estimators, where the problem of interest is distinguishing between two univariate distributions. When the densities intersect at a single point, optimal bandwidth choice depends on curvatures of the densities at that point. The problem of empirical bandwidth selection and classifying data in the tails of a distribution are also addressed.

• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.307-313
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• 2000

Suppose we have a set of data X1, ···, Xn and employ kernel density estimator to estimate the marginal density of X. in this article bandwith selection problem for kernel density estimator is examined closely. In particular the Kullback-Leibler method (a bandwith selection methods based on average square error (ASE)) is considered.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.179-188
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• 1998

Local polynomial regression estimation is the most popular one among kernel type regression estimator. In local polynomial regression function esimation bandwidth selection is crucial problem like the kernel estimation. When the regression curve has complicated structure variable bandwidth selection will be appropriate. In this paper, we propose a variable bandwidth selection method fully data driven. We will choose the bandwdith by selecting minimising estiamted MSE which is estimated by the pilot bandwidth study via croos-validation method. Monte carlo simulation was conducted in order to show the superiority of proposed bandwidth selection method.

• Journal of Korea Water Resources Association
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• v.39 no.6 s.167
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• pp.495-502
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• 2006

The importance of the bandwidth selection has been more emphasized than the kernel function selection for nonparametric frequency analysis since the interpolation is more reliable than the extrapolation method. However, when the extrapolation method is being applied(i.e. recurrence interval more than the length of data or extreme probabilities such as $200{\sim}500$ years), the selection of the kernel function is as important as the selection of the bandwidth. So far, the existing kernel functions have difficulties for extreme value estimations because the values extrapolated by kernel functions are either too small or too big. This paper suggests a Modified Cauchy kernel function that is suitable for both interpolation and extrapolation as an improvement.