• Communications for Statistical Applications and Methods
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• v.26 no.6
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• pp.527-538
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• 2019

This paper considers the issue of obtaining the optimal design in Poisson regression model when the sample size is small. Poisson regression model is widely used for the analysis of count data. Asymptotic theory provides the basis for making inference on the parameters in this model. However, for small size experiments, asymptotic approximations, such as unbiasedness, may not be valid. Therefore, first, we employ the second order expansion of the bias of the maximum likelihood estimator (MLE) and derive the mean square error (MSE) of MLE to measure the quality of an estimator. We then define DM-optimality criterion, which is based on a function of the MSE. This criterion is applied to obtain locally optimal designs for small size experiments. The effect of sample size on the obtained designs are shown. We also obtain locally DM-optimal designs for some special cases of the model.

• Journal of Korean Society for Quality Management
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• v.24 no.4
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• pp.44-58
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• 1996

This paper presents optimal accelerated life test plans with different censoring times for exponential, Weibull, and lognormal lifetime distributions, respectively. For an optimal plan, low stress level, proportion of test units allocated and censoring time at each stress are determined such that the asymptotic variance of the maximum likelihood estimator of a certain quantile at use condition is minimized. The proposed plans are compared with the corresponding optimal plans with a common censoring time over range of parameter values. Computational results indicate that those plans are statistically optimal ones in terms of accuracy of estimator when total censoring times of two plans are equal.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.673-683
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• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.9 no.1
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• pp.75-82
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• 1991

The objective of this paper is to investigate the optimal Robust estimation and scale estimator that could be used to treat the gross errors in a self calibrating bundle adjustment. In order to test the variability in performance of the different weighting schemes in accurately detecting gross error, five robust estimation methods and three types of scale estimators were used. And also, two difference control point patterns(high density control, sparse density control) and three types of gross errors(4$\sigma o$, 20$\sigma o$, 50$\sigma o$) were used for comparison analysis. As a result, Anscombe's robust estimation produced the best results in accuracy among the robust estimation methods considered. when considering the scale estimator about control point patterns, It can be seen that Type II scale estimator provided the best accuracy in high density control pattern. On the other hand, In the case of sparse density control pattern, Type III scale estimator showed the best results in accuracy. Therefore it is expected to apply to robustified bundle adjustment using the optimal scale estimator which can be used for eliminating the gross error in precise structure analysis.

• Proceedings of the KIEE Conference
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• 2006.04a
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• pp.18-20
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• 2006

The statistics for the neighbor differences between the particular pixels and their neighbors are introduced. They are incorporated into the filter to remove additive Gaussian noise contaminating images. The derived denoising method corresponds to the maximum likelihood estimator for the heavy-tailed Gaussian distribution. The error norm corresponding to our estimator from the robust statistics is equivalent to Huber's minimax norm. Our estimator is also optimal in the respect of maximizing the efficacy under the above noise environment.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.2
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• pp.210-217
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• 1990

For the failure detection of dynamic systems, processing the residuals from the observer of the estimator is the most general method. A failure detection method which use an adaptive predictor to separate the effect of sensor failure from the additive noise in the residuals of a Kalman filter that is employed as an estimator of a dynamic system is addressed here. In the method, the property of the residuals of an optimal Kalman estimator is exploited. The simulation results of this method shows that the proposed method is superior to the sequential probability ratio test for a small failure magnitude.

• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.551-561
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• 2001

This paper deals with the asymptotic properties for statistical inferences of the parameters in nonlinear regression models. As an optimal criterion for robust estimators of the regression parameters, the regression quantile method is proposed. This paper defines the regression quintile estimators in the nonlinear models and provides simple and practical sufficient conditions for the asymptotic normality of the proposed estimators when the parameter space is compact. The efficiency of the proposed estimator is especially well compared with least squares estimator, least absolute deviation estimator under asymmetric error distribution.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.271-282
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• 1996

this paper deal with the estimation of the power spectral density function of time series. A kernel estimator which is based on local average is defined and the rates of convergence of the pointwise, $$L_2$-norm; and; $L{\infty}$-norm associated with the estimator are investigated by restricting as to kernels with suitable assumptions. Under appropriate regularity conditions, it is shown that the optimal rate of convergence for 0$N^{-r}$ both in the pointwiseand $$L_2$-norm, while; $N^{r-1}(logN)^{-r}$is the optimal rate in the $L{\infty}-norm$. Some examples are given to illustrate the application of main results.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.39-44
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• 2002

We compare MISE of the MLE, UMVUE, invariantly optimal estimator and Jacknife estimator for the reliability function of the Weibull distribution when the sample size is small.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.251-269
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• 1994

In this paper we extend Kim and Pollard's cube root asymptotics to other rates of convergence, to establish an asymptotic theory for a multidimensional mode estimator based on uniform kernel with shrinking bandwidths. We obtain rates of convergence depending on shrinking rates of bandwidth and non-normal limit distributions. Optimal decreasing rates of bandwidth are discussed.