• Communications for Statistical Applications and Methods
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• 제21권5호
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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 Statistical Society
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• 제30권3호
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• pp.453-465
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• 2001

It is often the case that one wants to estimate parameters of the distribution which follows certain parametric model, while the dta are contaminated. it is well known that the maximum likelihood estimators are not robust to contamination. Basuet al.(1998) proposed a robust method called the minimum density power divergence estimation. In this paper, we investigate data-driven selection of the tuning parameter $\alpha$ in the minimum density power divergence estimation. A criterion is proposed and its performance is studied through the simulation. The simulation includes three cases of estimation problem.

• Communications for Statistical Applications and Methods
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• 제20권4호
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• pp.311-319
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• 2013

Cooray and Ananda (2005) proposed a composite lognormal-Pareto model to analyze loss payment data in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density. In this paper, we implement the minimum density power divergence estimation for the composite lognormal-Pareto density. We compare the performances of the minimum density power divergence estimator (MDPDE) and the maximum likelihood estimator (MLE) by simulations and an example. The minimum density power divergence estimator performs reasonably well against various violations in the distribution. The minimum density power divergence estimator better fits small observations and better resists against extraordinary large observations than the maximum likelihood estimator.

• 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.

• Communications for Statistical Applications and Methods
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• 제14권2호
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• pp.267-280
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• 2007

In this paper, we consider the robust estimation for diffusion processes when the sample is observed discretely. As a robust estimator, we consider the minimizing density power divergence estimator (MDPDE) proposed by Basu et al. (1998). It is shown that the MDPDE for diffusion process is weakly consistent. A simulation study demonstrates the robustness of the MDPDE.

• 응용통계연구
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• 제27권3호
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• pp.397-406
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• 2014

최소밀도함수승간격 추정법은 Baus 등 (1998)에 의해 처음 소개된 이후 많은 관심의 대상이 되었다. 최소밀도함수승간격 추정량은 우수한 로버스트 성질을 갖고 효율성도 최우추정량에 필적한 것으로 알려져 있다. 본 논문에서는 생물정보학에서 사용되는 노말-지수 분포에 근거한 추정량을 최소밀도함수승간격 추정법을 사용하여 구하는 방법을 다루고자 한다. 그런데 그 과정에서 간격을 적분을 통해 구하는 것이 매우 어려움으로 인해 직접적인 적분 대신 라플라스 근사를 시도할 것을 제안한다. 그 결과 추정량이 다소 효율성이 줄어들지만 로버스트 성질을 갖고 있음을 수학적 방법과 모의실험을 통하여 보였다.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.1159-1165
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• 2005

Basu et al. (1998) proposed a new density-based estimator, called the minimum density power divergence estimator (MDPDE), which avoid the use of nonparametric density estimation and associated complication such as bandwidth selection. Woodward et al. (1995) examined the minimum Hellinger distance estimator (MHDE), proposed by Beran (1977), in the case of estimation of the mixture proportion in the mixture of two normals. In this article, we introduce the MDPDE for a mixture proportion, and show that both the MDPDE and the MHDE have the same asymptotic distribution at a model. Simulation study identifies some cases where the MHDE is consistently better than the MDPDE in terms of bias.

• Journal of Welding and Joining
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• 제9권1호
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• pp.32-39
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• 1991

A 200W pulsed Nd: YAG laser for fine welding was developed. The important laser parameters such as laser peak power, average power, pulse width, and pulse energy for welding were studied. In order to obtain the sufficient laser power density for welding, thermal lensing effects were analyzed and a laser resonator with laser beam divergence was designed. The power supply unit was designed to support up to 7kW input. The pulse control unit was developed using a GTO thyristor and could control over 100kW input power to obtain 3.5kW peak power laser. Also due to the GTO thyristor the pulse width could be varied continuously from 0.1 to 20 msec and maximum repetition rate was as high as 300pps.

• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.687-696
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• 2003

This article presents a new family of the estimating functions related with minimum distance estimations, and discusses its relationship to the family of the minimum density power divergence estimating equations. Two representative minimum distance estimations; the minimum $L_2$ distance estimation and the minimum Hellinger distance estimation are studied in the light of the theory of estimating equations. Despite of the desirable properties of minimum distance estimations, they are not widely used by general researchers, because theories related with them are complex and are hard to be computationally implemented in real problems. Hopefully, this article would be a help for understanding the minimum distance estimations better.

• Communications for Statistical Applications and Methods
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• 제30권6호
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• pp.531-550
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• 2023

The estimation of extreme quantiles is one of the main objectives of statistics of extremes (which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regression model. The proposed estimator was compared with two estimators of extreme quantiles in the literature in a simulation study. The results show that the proposed estimator is stable to the choice of the number of top order statistics and show lesser bias and mean square error compared to the existing extreme quantile estimators. Practical application of the proposed estimator is illustrated with data from the pedochemical and insurance industries.