• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.83-91
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• 1993

Random elements in $L^1(R)$ and some properties of $L^1(R)$ space are investigated with application to kernel density estimators. A weak law of large numbers for compact uniformly integrable random elements is introduced for further application.

• 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.2 no.1
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• pp.99-111
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• 1995

It is shown that the adaptive kernel methods can potentially produce superior density estimates to the fixed one. In using the adaptive estimates, problems pertain to the initial choice of the estimate can be solved by iteration. Also, simultaneous recommended for variety of distributions. Some data-based method for the choice of the parameters are suggested based on simulation study.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.408-413
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• 2005

A new methodology for discrete non-Gaussian probability density estimation is investigated in this paper based on a dynamic Bayesian network (DBN) and kernel functions. The estimator consists of a DBN in which the transition distribution is represented with kernel functions. The estimator parameters are determined through a recursive learning algorithm according to the maximum likelihood (ML) scheme. A discrete-type Poisson distribution is generated in a simulation experiment to evaluate the proposed method. In addition, an unknown probability density generated by nonlinear transformation of a Poisson random variable is simulated. Computer simulations numerically demonstrate that the method successfully estimates the unknown probability distribution function (PDF).

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.5
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• pp.381-389
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• 2017

The kernel density was determined based on sampling points obtained in a Markov chain simulation and was assumed to be an important sampling function. A Kriging metamodel was constructed in more detail in the vicinity of a limit state. The failure probability was calculated based on importance sampling, which was performed for the Kriging metamodel. A pre-existing method was modified to obtain more sampling points for a kernel density in the vicinity of a limit state. A stable numerical method was proposed to find a parameter of the kernel density. To assess the completeness of the Kriging metamodel, the possibility of changes in the calculated failure probability due to the uncertainty of the Kriging metamodel was calculated.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.987-994
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• 2011

From the point view of credit evaluation whose population is divided into the default and non-default state, two methods are considered to estimate conditional distribution functions: one is to estimate under the assumption that the data is followed the mixture normal distribution and the other is to use the kernel density estimation. The parameters of normal mixture are estimated using the EM algorithm. For the kernel density estimation, five kinds of well known kernel functions and four kinds of the bandwidths are explored. In addition, the corresponding ROC functions are obtained based on the estimated distribution functions. The goodness-of-fit of the estimated distribution functions are discussed and the performance of the ROC functions are compared. In this work, it is found that the kernel distribution functions shows better fit, and the ROC function obtained under the assumption of normal mixture shows better performance.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.32 no.3
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• pp.245-251
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• 2014

As delineating market areas of retail businesses has become an interesting topic in marketing field, Lee and Lee recently suggested a noteworthy method, which applied the hydrological analysis of geographical information system (GIS), based on Christaller's central place theory. They used a digital elevation model (DEM) which inverted the kernel density of retail businesses, which was measured by using bandwidths of pre-determined 500, 1000 and 5000 m, respectively. In fact, their method is not a fully data-based approach in that they used pre-determined kernel bandwidths, however, this paper has been planned to improve Lee and Lee's method by using a kind of data-based approach of the L-index that describes clustering level of point feature distribution. The case study is implemented to automobile-related retail businesses in Seoul, Korea with selected Kernel bandwidths, 1211.5, 2120.2 and 7067.2 m from L-index analysis. Subsequently, the kernel density is measured, the density DEM is created by inverting it, and boundaries of market areas are extracted. Following the study, analysis results are summarized as follows. Firstly, the L-index can be a useful tool to complement the Lee and Lee's market area analysis method. At next, the kernel bandwidths, pre-determined by Lee and Lee, cannot be uniformly applied to all kinds of retail businesses. Lastly, the L-index method can be useful for analyzing the space structure of market areas of retail businesses, based on Christaller's central place theory.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.435-444
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• 2014

The most widely used optimal bandwidth is known to minimize the mean integrated squared error(MISE) of a kernel density estimator from a true density. In this article proposes, we propose a bandwidth which asymptotically minimizes the mean integrated density power divergence(MIDPD) between a true density and a corresponding kernel density estimator. An approximated form of the mean integrated density power divergence is derived and a bandwidth is obtained as a product of minimization based on the approximated form. The resulting bandwidth resembles the optimal bandwidth by Parzen (1962), but it reflects the nature of a model density more than the existing optimal bandwidths. We have one more choice of an optimal bandwidth with a firm theoretical background; in addition, an empirical study we show that the bandwidth from the mean integrated density power divergence can produce a density estimator fitting a sample better than the bandwidth from the mean integrated squared error.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.705-712
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• 2005

Entropy is the basic concept of information theory. It is well defined for random varibles with known probability density function(pdf). For given data with unknown pdf, entropy should be estimated. Usually, estimation of entropy is based on the approximations. In this paper, we consider a kernel based approximation and compare it to the cumulant approximation method for several distributions. Monte carlo simulation for various sample size is conducted.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.265-276
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• 1996

The nonparametric deconvolution problems are studied to recover an unknown density when the data are contaminated with Gaussian error. We propose the estimator which is a linear combination of kernel type estimates of derivertives of the observed density function. We show that this estimator is consistent and also consider the properties of estimator at small sample by simulation.