• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.929-937
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• 2003

Kernel type estimations of discontinuity point at an unknown location in regression function or its derivatives have been developed. It is known that the discontinuity point estimator based on $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a zero value at the point 0 makes a poor asymptotic behavior. Further, the asymptotic variance of $Gasser-M\ddot{u}ller$ regression estimator in the random design case is 1.5 times larger that the one in the corresponding fixed design case, while those two are identical for the local polynomial regression estimator. Although $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a non-zero value at the point 0 for the modification is used, computer simulation show that this phenomenon is also appeared in the discontinuity point estimation.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.147-158
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• 2004

Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation on the modulus of continuity. This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.12.1-12
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• 2003

Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation On the modulus of continuity This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.111-120
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• 2016

In usual, the discontinuous variance function was estimated nonparametrically using a kernel type estimator with data sets split by an estimated location of the change point. Kang et al. (2000) proposed the Gasser-$M{\ddot{u}}ller$ type kernel estimator of the discontinuous regression function using the adjusted observations of response variable by the estimated jump size of the change point in $M{\ddot{u}}ller$ (1992). The adjusted observations might be a random sample coming from a continuous regression function. In this paper, we estimate the variance function using the Nadaraya-Watson kernel type estimator using the adjusted squared residuals by the estimated location of the change point in the discontinuous variance function like Kang et al. (2000) did. The rate of convergence of integrated squared error of the proposed variance estimator is derived and numerical work demonstrates the improved performance of the method over the exist one with simulated examples.

• Communications for Statistical Applications and Methods
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• v.23 no.3
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• pp.189-201
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• 2016

In survival analysis, the Nelson-Aalen estimator and Peterson estimator are often used to estimate a cumulative hazard function in randomly right censored data. In this paper, we suggested the smoothing version of the cumulative hazard function estimators using a Bezier curve. We compare them with the existing estimators including a kernel smooth version of the Nelson-Aalen estimator and the Peterson estimator in the sense of mean integrated square error to show through numerical studies that the proposed estimators are better than existing ones. Further, we applied our method to the Cox regression where covariates are used as predictors and suggested a survival function estimation at a given covariate.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.403-412
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• 2004

We obtain a kernel quantile process based on the kernel quantile estimator and prove the uniform consistency of the kernel quantile process by developing that of the usual sample quantile process. We apply our result to the classical kernel type processes.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.115-124
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• 2014

In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $Y{\geq}T$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $n^{-1/6}$ modulo logarithmic term. We have also investigated this normal approximation rate via a 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).

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.19-24
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• 1994

Let P be a probability measure on the real line with Lebesque-density f. The usual estimator of the distribution function (≡df) of P for the sample $\chi$$_1$,…, $\chi$$\_$n/ is the empirical df: F$\_$n/(t)=(equation omitted). But this estimator does not take into account the smoothness of F, that is, the existence of a density f. Therefore, one should expect that an estimator which is better adapted to this situation beats the empirical df with respect to a reasonable measure of performance.(omitted)