• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.51-68
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• 2020

In this paper, the author considers the nonparametric regression model with negatively orthant dependent random variables. The wavelet procedures are developed to estimate the regression function. For the wavelet estimator of unknown function g(·), the almost sure consistency is derived and the complete consistency is established under the mild conditions. Our results generalize and improve some known ones for independent random variables and dependent random variables.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.57-72
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• 1999

Falk(1994) showed that the asymptotic efficiency of the Pickands estimator of the extreme value index $\beta$ can considerably be improved by a simple convex combination. In this paper we propose an alternative estimator of $\beta$ which is as asymptotically efficient as the optimal convex combination of the Pickands estimators but has a better finite-sample performance. We prove consistency and asymptotic normality of the proposed estimator. Monte Carlo simulations are conducted to compare the finite-sample performances of the proposed estimator and the optimal convex combination estimator.

• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.261-270
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• 2003

This paper introduces a new density estimator which is Hellinger consistent under a simple condition. A number of issues are discussed, such as extension to Kullback-Leibler consistency, robustness, the Bayes version of the estimator and the maximum likelihood case. An illustration is presented.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.653-664
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• 2000

The problem of inference about the unknown change-point with a change in mean is considered. We suggest a nonparametric change-point estimator using window and prove its consistency when the errors are from the distribution with the mean zero and the common variance. a comparison study is done by simulation on the mean, the variance, and the proportion of matching the true change-points.

• Journal of the Korean Data and Information Science Society
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• v.5 no.2
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• pp.59-74
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• 1994

The hazard ratio may be useful as a descriptive measure to compare the hazard experience of a treatment group with that of a control group. In this paper, we propose a kernel estimator of hazard ratio with censored survival data. The uniform consistency and asymptotic normality of the proposed estimator are proved by using counting process approach. In order to assess the performance of the proposed estimator, we compare the kernel estimator with Cox estimator and the generalized rank estimators of hazard ratio in terms of MSE by Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
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• v.15 no.1
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• pp.273-284
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• 2004

Bayes estimation of parameters is considered for two independent exponential distributions with ordered means. Order restricted Bayes estimators for means are obtained with respect to inverted gamma, noninformative prior and uniform prior distributions, and their asymptotic properties are established. It is shown that the maximum likelihood estimator, restricted maximum likelihood estimator, unrestricted Bayes estimator, and restricted Bayes estimator of the mean are all consistent and have the same limiting distribution. These estimators are compared with the corresponding unrestricted Bayes estimators by Monte Carlo simulation.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.109-114
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• 2002

In this paper we propose a change-point estimator with left and right regressions using the sample Fourier coefficients on the orthonormal bases. The asymptotic properties of the proposed change-point estimator are established. The limiting distribution and the consistency of the estimator are derived.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.357-365
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• 2011

This paper investigates a penalized likelihood method for estimating the parameter of normal mixtures in multivariate settings with full covariance matrices. The proposed model estimates the number of components through the addition of a penalty term to the usual likelihood function and the construction of a penalized likelihood function. We prove the consistency of the estimator and present the simulation results on the multi-dimensional nor-mal mixtures up to the 8-dimension.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.633-641
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• 2001

The least squares method is usually applied when estimating the parameters in the regression models. However the least square estimator is not very efficient when the distribution of the error is skewed. In this paper, we propose the asymmetric least square estimator for a particular nonlinear time series regression model, and give the simple and practical sufficient conditions for the strong consistency of the estimators.

• Journal of the Korean Statistical Society
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• v.34 no.4
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• pp.273-280
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• 2005

In this paper we introduce an estimator of the second order parameter characterizing the tail behavior of probability distributions and prove its consistency.