• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.313-321
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• 2004

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts et al. (2000) presented T=${{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2$ as a test statistic with the local least square polynomial estimator ${{p}_{i}}^{*}$, and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood polynomial estimator ${{\hat{p}}_{i}}$, however, guarantees positive estimates for cell probabilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T_1={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of $T_2={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ where the minimum expected cell frequency is very small.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.489-498
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• 1998

The influence of observations the on the goodness-of-fit test in maximum likelihood factor analysis is investigated by using the local influence method. under an appropriate perturbation the test statistic forms a surface. One of main diagnostics is the maximum slope of the perturbed surface the other is the direction vector cor-responding to the curvature. These influence measures provide the information about jointly influence measures provide the information about jointly influential observations as well as individ-ually influential observations.

• Journal of the Korean Statistical Society
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• v.29 no.1
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• pp.9-16
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• 2000

This article addresses the problem of maximum likelihood estimation in ARCH regression with lagged dependent variables. Some topics in asymptotics of the model such as uniform expansion of likelihood function and construction of a class of MLE are discussed, and the regularity property of MLE is obtained. The error process here is possibly non-Gaussian.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.145-151
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• 1996

The local behaviour of the surface formed by the perturbed maximum likelihood estimator of the squared Mahalanobis distance is investigated. The study of the local behaviour allows a simultaneous perturbation on the samples of interest and it is effective in identifying influential observations.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.273-283
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• 2006

In bioassay, the response curve is usually assumed monotone increasing, but its exact form is unknown, so it is very difficult to select the proper functional form for the parametric model. Therefore, we should probably use the nonparametric regression model rather than the parametric model unless we have at least the partial information about the true response curve. However, it is well known that the nonparametric regression estimate is not necessarily monotone. Therefore the monotonizing transformation technique is of course required. In this paper, we compare the finite sample properties of the monotone transformation methods which can be applied to the local linear quasi-likelihood response curve estimate.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.217-223
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• 2013

Two influence diagnostic methods for the common mean model are proposed. First, an investigation of the influence of observations according to minor perturbations of the common mean model is made by adapting the local influence method which is based on the likelihood displacement. It is well known that the maximum likelihood estimates are in general sensitive to influential observations. Case-deletions can be a candidate for detecting influential observations. However, the maximum likelihood estimators are iteratively computed and therefore case-deletions involve an enormous amount of computations. An approximation by Newton's method to the maximum likelihood estimator obtained after a single observation was deleted can reduce much of computational burden, which will be treated in this work. A numerical example is given for illustration and it shows that the proposed diagnostic methods can be useful tools.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.116-119
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• 2005

As to the synthetical estimation of land covering parameters or the compounded land covering classification for multi-resolution satellite data, former researches mainly adopted linear or nonlinear regression models to describe the regression relationship of land covering parameters caused by the degradation of spatial resolution, in order to improve the retrieval accuracy of global land covering parameters based on 1;he lower resolution satellite data. However, these methods can't authentically represent the complementary characteristics of spatial resolutions among different satellite data at arithmetic level. To resolve the problem above, a new compounded land covering classification method at arithmetic level for multi-resolution satellite data is proposed in this .paper. Firstly, on the basis of unsupervised clustering analysis of the higher resolution satellite data, the likelihood distribution scatterplot of each cover type is obtained according to multiple-to-single spatial correspondence between the higher and lower resolution satellite data in some local test regions, then Parzen window approach is adopted to derive the real likelihood functions from the scatterplots, and finally the likelihood functions are extended from the local test regions to the full covering area of the lower resolution satellite data and the global covering area of the lower resolution satellite is classified under the maximum likelihood rule. Some experimental results indicate that this proposed compounded method can improve the classification accuracy of large-scale lower resolution satellite data with the support of some local-area higher resolution satellite data.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.743-752
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• 2002

The estimation of the response curve is the important problem in the quantal bioassay. When we estimate the response curve, we determine the design points in advance of the experiment. Then naturally we have a question of which design would be optimal. As a response curve estimator, locally weighted quasi-likelihood estimator has several more appealing features than the traditional nonparametric estimators. The optimal design density for the locally weighted quasi-likelihood estimator is derived and its ability both in theoretical and in empirical point of view are investigated.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.347-355
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• 2001

We propose a method for detecting influential observations that have a large influence on the likelihood ratio test statistic for the two sets of variables are uncorrelated with one another. For this purpose we derive a local influence measure for the likelihood ratio test statistic under certain perturbation scheme. An illustrative example is given to show the effectiveness of the proposed method on the identification of influential observations.

• Journal of the Korean Statistical Society
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• v.27 no.1
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• pp.91-100
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• 1998

A method of estimating probability density using regression tools is presented here. It is based on equal-length binning and locally weighted approximate likelihood for bin counts. The method is particularly useful for densities with bounded supports, where it automatically corrects edge effects without using boundary kernels.