• 대한수학회보
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• 제40권3호
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• pp.373-383
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• 2003

We investigate a uniform local asymptotic normality for likelihood ratio processes based on an independent and identically distributed local asymptotic problem. Our tool is an empirical process theory.

• Journal of the Korean Statistical Society
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• 제20권1호
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• pp.85-92
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• 1991

A set of conditions ensuring local asymptotic normality for independent but not necessarily identically distributed observations in semiparametric models is presented here. The conditions are turned out to be more direct and easier to verify than those of Oosterhoff and van Zwet(1979) in semiparametric models. Examples considered include the simple linear regression model and Cox's proportional hazards model without censoring where the covariates are not random.

• Journal of the Korean Statistical Society
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• 제26권4호
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• pp.467-476
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• 1997

The two-sample t-test is not expected to be optimal when the two samples are not drawn from normal populations. According to Box and Cox (1964), the transformation is estimated to enhance the normality of the tranformed data. We investigate the asymptotic relative efficiency of the ordinary t-test versus t-test applied transformation introduced by Yeo and Johnson (1997) under Pitman local alternatives. The theoretical and simulation studies show that two-sample t-test using transformed date gives higher power than ordinary t-test for location-shift models.

• Journal of the Korean Statistical Society
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• 제33권3호
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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 the Korean Statistical Society
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• 제30권3호
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• pp.387-406
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• 2001

Adaptive estimators for a class of nonlinear time series models has been proposed by several authors. Koul and Schick(1997) proposed the adaptive estimators without sample splitting for location-type time series models. They also showed by simulation that the adaptive estimators without sample splitting have smaller mean squared errors than those of the adaptive estimators with sample splitting. the present paper generalized the result in a case of location-scale type nonlinear time series models by simulation.