• Journal for History of Mathematics
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• v.16 no.3
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• pp.95-100
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• 2003

The recent surge of interest in the more technical aspects of nonparametric density estimation and nonparametric regression estimation has brought the subject into public view. In this paper, we investigate the general concept of the nonparametric density estimation, the nonparametric regression estimation and its performance criteria.

• 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.

• 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.

• 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.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.129-140
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• 2000

Wavelets constitute a new orthogonal system which has direct application in density estimation. We introduce a brief wavelet density estimation and summarize some asymptotic results. An application to mixture normal distributions is implemented with S-Plus.

• 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.18 no.4
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• pp.457-465
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• 2011

Sample entropy (Vasicek, 1976) has poor performance, and several nonparametric entropy estimators have been proposed as alternatives. In this paper, we consider a piecewise uniform density function based on quantiles, which enables us to evaluate entropy in each interval, and study the poor performance of the sample entropy in terms of the poor estimation of lower and upper quantiles. Then we propose some improved entropy estimators by simply modifying the quantile estimators, and compare their performances with some existing estimators.

• 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 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.

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.31-36
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• 2010

3D point data acquired from laser scan or stereo vision can be quite noisy. A preprocessing step is often needed before a surface reconstruction algorithm can be applied. In this paper, we propose a nonparametric approach for noisy point data preprocessing. In particular, we proposed an anisotropic kernel based nonparametric density estimation method for outlier removal, and a hill-climbing line search approach for projecting data points onto the real surface boundary. Our approach is simple, robust and efficient. We demonstrate our method on both real and synthetic point datasets.