• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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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).

• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.349-360
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• 1995

This paper deals with the robustness properties of the minimum disparity estimation in linear regression models. The estimators defined as statistical quantities whcih minimize the blended weight Hellinger distance between a weighted kernel density estimator of the residuals and a smoothed model density of the residuals. It is shown that if the weights of the density estimator are appropriately chosen, the estimates of the regression parameters are robust.

• International Journal of Control, Automation, and Systems
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• 제6권1호
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• pp.109-118
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• 2008

We present two estimators for discrete non-Gaussian and nonstationary probability density estimation based on a dynamic Bayesian network (DBN). The first estimator is for off line computation and consists of a DBN whose transition distribution is represented in terms of kernel functions. The estimator parameters are the weights and shifts of the kernel functions. The parameters are determined through a recursive learning algorithm using maximum likelihood (ML) estimation. The second estimator is a DBN whose parameters form the transition probabilities. We use an asymptotically convergent, recursive, on-line algorithm to update the parameters using observation data. The DBN calculates the state probabilities using the estimated parameters. We provide examples that demonstrate the usefulness and simplicity of the two proposed estimators.

• 대한수학회보
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• 제54권1호
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• pp.343-358
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• 2017

Let {$X_i$} be a sequence of stationary ${\alpha}-mixing$ random variables with probability density function f(x). The recursive kernel estimators of f(x) are defined by $$\hat{f}_n(x)={\frac{1}{n\sqrt{b_n}}{\sum_{j=1}^{n}}b_j{^{-\frac{1}{2}}K(\frac{x-X_j}{b_j})\;and\;{\tilde{f}}_n(x)={\frac{1}{n}}{\sum_{j=1}^{n}}{\frac{1}{b_j}}K(\frac{x-X_j}{b_j})$$, where 0 < $b_n{\rightarrow}0$ is bandwith and K is some kernel function. Under appropriate conditions, we establish the Berry-Esseen bounds for these estimators of f(x), which show the convergence rates of asymptotic normality of the estimators.

• Communications for Statistical Applications and Methods
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• 제21권2호
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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.

• Journal of the Korean Data and Information Science Society
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• 제14권2호
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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.

• Communications for Statistical Applications and Methods
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• 제16권6호
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• pp.989-995
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• 2009

Basu et al. (1998) proposed the minimum divergence estimating method which is free from using the painful kernel density estimator. Their proposed class of density power divergences is indexed by a single parameter $\alpha$ which controls the trade-off between robustness and efficiency. In this article, (1) we introduce a new large class the minimum squared distance which includes from the minimum Hellinger distance to the minimum $L_2$ distance. We also show that under certain conditions both the minimum density power divergence estimator(MDPDE) and the minimum squared distance estimator(MSDE) are asymptotically equivalent and (2) in finite samples the MDPDE performs better than the MSDE in general but there are some cases where the MSDE performs better than the MDPDE when estimating a location parameter or a proportion of mixed distributions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제1권1호
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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)

• Journal of the Korean Statistical Society
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• 제34권1호
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• pp.49-60
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• 2005

In this paper we introduce a nonparametric method for estimating the probability density function of detection distances in line transect sampling. The estimator is obtained using a frequency histogram density estimation method. The asymptotic properties of the proposed estimator are derived and compared with those of the kernel estimator under the assumption that the data collected satisfy the shoulder condition. We found that the asymptotic mean square error (AMSE) of the two estimators have about the same convergence rate. The formula for the optimal histogram bin width is derived which minimizes AMSE. Moreover, the performances of the corresponding k-nearest-neighbor estimators are studied through simulation techniques. In the absence of our knowledge whether the shoulder condition is valid or not a new semi-parametric model is suggested to fit the line transect data. The performances of the proposed two estimators are studied and compared with some existing nonparametric and semiparametric estimators using simulation techniques. The results demonstrate the superiority of the new estimators in most cases considered.

• 대한전자공학회논문지SP
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• 제48권6호
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• pp.124-132
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• 2011

현대 전자전에서 레이더 신호 환경은 매우 복잡하고 고밀도화 되어 가고 있다. 이러한 신호로부터 원래의 방사체로 각각 분리하여 분석하고 식별하기 위한 전자전지원을 위해서는 신뢰성있는 신호분석 기법이 요구된다. 본 논문에서는 전자전지원의 신호분석 단계에서 신뢰성을 보장하며 신호처리 비용을 줄일 수 있는 새로운 레이더 신호 그룹화 알고리즘을 제안하였다. 제안된 기법은 주파수 변조 특성에 대한 통계적 분포 특성을 활용하여 수신 신호로부터 커널 밀도 추정 방식을 이용하여 신호 그룹화한다. 제안된 기법에 대해 실험 결과를 통해 우수한 성능을 보유함을 확인하였다.