• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.939-946
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• 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
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• v.2 no.2
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• pp.243-248
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• 1995

The problem of optimal design for a nonparametric regression with binary data is considered. The aim of the statistical analysis is the estimation of a quantal response surface in two dimensions. Bias, variance and IMSE of kernel estimates are derived. The optimal design density with respect to asymptotic IMSE is constructed.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.65-73
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• 2000

Kernel estimator is very popular in nonparametric density estimation. In this paper we propose an estimator which reduces the bias to the fourth power of the bandwidth, while the variance of the estimator increases only by at most moderate constant factor. The estimator is fully nonparametric in the sense of convex combination of three kernel estimators, and has good numerical properties.

• 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 Data and Information Science Society
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• v.14 no.2
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• pp.247-255
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• 2003

Hypothesis testing for the equality of two distributions were considered. Nonparametric kernel density estimates were used for testing equality of distributions. Cross-validatory choice of bandwidth was used in the kernel density estimation. Sampling distribution of considered test statistic were developed by resampling method, called the bootstrap. Small sample Monte Carlo simulation were conducted. Empirical power of considered tests were compared for variety distributions.

• 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.31 no.2
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• pp.261-276
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• 2002

Probability density or its derivatives may have a discontinuity/change point at an unknown location. We propose a method of estimating the location and the jump size of the discontinuity point based on kernel type density or density derivatives estimators with one-sided equivalent kernels. The rates of convergence of the proposed estimators are derived, and the finite-sample performances of the methods are illustrated by simulated examples.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.451-457
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• 2010

This paper considers the problem of nonparametric deconvolution density estimation when sample observa-tions are contaminated by double exponentially distributed errors. Three different deconvolution density estima-tors are introduced: a weighted kernel density estimator, a kernel density estimator based on the support vector regression method in a RKHS, and a classical kernel density estimator. The performance of these deconvolution density estimators is compared by means of a simulation study.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.15-20
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• 2004

We investigate the unbiasedness and consistency as the statistical properties of density estimators. We show histogram, kernel density estimation, and local adaptive smoothing as density smoothing in this paper. Also, the early and recent research on nonparametric density estimation is described and discussed.

• Journal of the Korean Statistical Society
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• v.10
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• pp.140-144
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• 1981

This paper approximates to a kernel density estimate by a truncated series of expansion involving Hermite polynomials, since this could ease the computing burden involved in the kernel-based density estimation. However, this truncated series may give a multimodal estimate when we are estiamting unimodal density. In this paper we will show a way to insure the truncated series to be positive and unimodal so that the approximation to a kernel density estimator would be maeningful.