• 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 Statistical Society
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• v.30 no.3
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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.

• The Korean Journal of Applied Statistics
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• v.27 no.3
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• pp.397-406
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• 2014

The minimum density power divergence estimation has been a popular topic in the field of robust estimation for since Basu et al. (1988). The minimum density power divergence estimator has strong robustness properties with the little loss in asymptotic efficiency relative to the maximum likelihood estimator under model conditions. However, a limitation in applying this estimation method is the algebraic difficulty on an integral involved in an estimation function. This paper considers a minimum density power divergence estimation method with approximated divergence avoiding such difficulty. As an example, we consider the normal-exponential convolution model introduced by Bolstad (2004). The estimated divergence in this case is too complicated; consequently, a Laplace approximation is employed to obtain a manageable form. Simulations and an empirical study show that the minimum density power divergence estimators based on an approximated estimated divergence for the normal-exponential model perform adequately in terms of bias and efficiency.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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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.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.453-465
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• 1997

The family of power-divergence statistics conditional on margins is considered for testing homogeneity of .tau. multinomial populations with equal sample size and the exact Bahadur slope is obtained. It is shown that the likelihood ratio test conditional on margins is the most Bahadur efficient among the family of power-divergence statistics.

• Communications for Statistical Applications and Methods
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• v.20 no.4
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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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• v.16 no.6
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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.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.743-752
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• 2004

In this paper, we develop the Bayesian model selection procedure using the reference prior for comparing two nested model such as the independent and intraclass models using the distance or divergence between the two as the basis of comparison. A suitable criterion for this is the power divergence measure as introduced by Cressie and Read(1984). Such a measure includes the Kullback -Liebler divergence measures and the Hellinger divergence measure as special cases. For this problem, the power divergence measure turns out to be a function solely of $\rho$, the intraclass correlation coefficient. Also, this function is convex, and the minimum is attained at $\rho=0$. We use reference prior for $\rho$. Due to the duality between hypothesis tests and set estimation, the hypothesis testing problem can also be solved by solving a corresponding set estimation problem. The present paper develops Bayesian method based on the Kullback-Liebler and Hellinger divergence measures, rejecting $H_0:\rho=0$ when the specified divergence measure exceeds some number d. This number d is so chosen that the resulting credible interval for the divergence measure has specified coverage probability $1-{\alpha}$. The length of such an interval is compared with the equal two-tailed credible interval and the HPD credible interval for $\rho$ with the same coverage probability which can also be inverted into acceptance regions of $H_0:\rho=0$. Example is considered where the HPD interval based on the one-at- a-time reference prior turns out to be the shortest credible interval having the same coverage probability.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.135-144
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• 2003

This work is concerned with comparison of the recently developed disparity measures for the partial association model in three dimensional categorical data. Data are generated by using simulation on each term in the log-linear model equation based on the partial association model, which is a proposed method in this paper. This alternative Monte Carlo methods are explored to study the behavior of disparity measures such as the power divergence statistic I(λ), the Pearson chi-square statistic X$^2$, the likelihood ratio statistic G$^2$, the blended weight chi-square statistic BWCS(λ), the blended weight Hellinger distance statistic BWHD(λ), and the negative exponential disparity statistic NED(λ) for moderate sample sizes. We find that the power divergence statistic I(2/3) and the blended weight Hellinger distance family BWHD(1/9) are the best tests with respect to size and power.

• Current Optics and Photonics
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• v.6 no.2
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• pp.191-195
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• 2022

We investigate the lateral far-field pattern characteristics, including divergence angle change and far-field pattern analysis as output power increases, of narrow-emitter-width 850 nm GaAs/AlGaAs laser diodes (LDs). Each LD has a cavity of 1200 and 1500 ㎛ and narrow emitter width of 2.4 ㎛ for the top and 4.6 ㎛ for the bottom. The threshold currents are 35 and 40 mA, and L-I kinks appear at power levels of 326 and 403 mW, respectively. The divergence angle tends to increase due to the occurrence of first-order lateral mode and the thermal lensing effect. But with the L-I kink, the divergence angle decreases and the far-field pattern becomes asymmetric. This is due to coherent superposition between the fundamental and the first-order lateral mode. We provide detailed explanations for these observations based on high-power laser diode simulation results.