• 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.28 no.3
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• pp.325-336
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• 1999

Collinearity among independent variables can have severe effects on the precision of response estimation for some region of interest in the experiments with mixture. A method of finding optimal linear restriction on regression parameter in linear model for mixture experiments in the sense of minimizing integrated mean squared error is studied. We use the formulation of optimal restrictions on regression parameters for estimating responses proposed by Park(1981) by transforming mixture components to mathematically independent variables.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.675-685
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• 2008

This paper studies two sequential procedures to estimate a monotone convex function using $L_2$ monotonization and uniform convexification; one, denoted by FMSC, monotonizes the data first and then, convexifis the monotone estimate; the other, denoted by FCSM, first convexifies the data and then monotonizes the convex estimate. We show that two shape modifiers are not commutable and so does FMSC and FCSM. We compare them numerically in uniform error(UE) and integrated mean squared error(IMSE). The results show that FMSC has smaller uniform error(UE) and integrated mean squared error(IMSE) than those of FCSC.

• 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.30 no.4
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• pp.585-595
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• 2001

A second-order response surface model is often used to approximate the relationship between a response factor and a set of explanatory factors. In this article, we deal with canonical analysis in response surface models. For the interpretation of the geometry of second-order response surface model, standard errors and confidence intervals for the eigenvalues of the second-order coefficient matrix play an important role. If the confidence interval for some eigenvalue includes 0 or the estimate of some eigenvalue is very small (near to 0) with respect to other eigenvalues, then we are able to delete the corresponding canonical factor. We propose a formulation of criterion which can be used to select canonical factors. This criterion is based on the IMSE(=Integrated Mean Squared Error). As a result of this method, we may approximately write the canonical factors as a set of some important explanatory factors.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.239-250
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• 1998

A method of finding optimal linear restriction on regression parameters in linear model for mixture experiments in the sense of minimizing integrated mean squared error is studied. We use the formulation of optimal restrictions on regression parameters for estimating responses proposed by Park(1981) by transforming mixture components to mathematically independent variables.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.327-336
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• 2001

This work concerns estimating a regression function, which is not linear, using aggregate data. In much of the empirical research, data are aggregated for various reasons before statistical analysis. In a traditional parametric approach, a linear estimation of the non-linear function with aggregate data can result in unstable estimators of the parameters. More serious consequence is the bias in the estimation of the non-linear function. The approach we employ is the kernel regression smoothing. We describe the conditions when the aggregate data can be used to estimate the regression function efficiently. Numerical examples will illustrate our findings.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.891-901
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• 1997

The objective of this research is to investigate the problem of goodness of fit testing based on nonparametric density estimation with a data-driven smoothing parameter. The small and large smaple properties of the proposed test statistic $Z_{mn}$ are investigated with the minimizer $\widehat{m}$ of the estimated mean integrated squared error by the Diggle and Hall (1986) method.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1049-1058
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• 2012

Nonparametric methods are often used as an alternative to parametric methods to estimate density function and regression function. In this paper we consider improved methods to select the Bezier points in Bezier curve smoothing that is shown to have the same asymptotic properties as the kernel methods. We show that the proposed methods are better than the existing methods through numerical studies.

• Journal of the Korean Statistical Society
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• v.20 no.2
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• pp.147-155
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• 1991

This paper treats a robust design criterion which minimizes the effects of outliers and model inadequacy, and investigates robust designs for some response surface designs. In order to develop a robust design criterion and robust design, the integrated mean squared error of *(equation omitted) over a region is utilized, where *(equation omitted). is the estimated response by the minimum bias estimation proposed by carson, Manson and Hader (1969) . According to the number of aberrant observations and their positions, the proposed criterion and designs are studied. Also further development of the proposed criterion is treated when outliers can occur in any position of a design.