• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.195-203
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• 2007

In this paper we propose support vector quantile regression (SVQR) for randomly right censored data. The proposed procedure basically utilizes iterative method based on the empirical distribution functions of the censored times and the sample quantiles of the observed variables, and applies support vector regression for the estimation of the quantile function. Experimental results we then presented to indicate the performance of the proposed procedure.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.57-65
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• 1999

In a resent paper, Na, Lee and Kim(1998) develop a test statistic for testing whether or not the mean residual life changes its trend based on complete data and show that the new test performs better than previously known tests. In this paper, we extend their test to the randomly censored data. The asymptotic normality of the test statistic is established. Monte Carlo simulations are conducted to compare our test with a previously known test by the power of tests.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.883-891
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• 2011

For survival data we sometimes want to test a log normality hypothesis that can be changed into normality by transforming the survival data. Hence the Shapiro-Wilk type statistic for normality is generalized to randomly censored data based on the Kaplan-Meier product limit estimate of the distribution function. Koziol and Green (1976) derived Cram$\acute{e}$r-von Mises statistic's randomly censored version under the simpl hypothesis. These two test statistics are compared through a simulation study. As for the distribution of censoring variables, we consider Koziol and Green (1976)'s model and other similar models. Through the simulation results, we can see that the power of the proposed statistic is higher than that of Koziol-Green statistic and that the proportion of the censored observations (rather than the distribution of censoring variables) has a strong influence on the power of the proposed statistic.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.99-106
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• 1999

In this paper, the spline hazard rate model to the randomly censored data is introduced. The unknown hazard rate function is expressed as a linear combination of B-splines which is constrained to be linear(or constant) in tails. We determine the coefficients of the linear combination by maximizing the likelihood function. The number of knots are determined by Bayesian Information Criterion. Examples using simulated data are used to illustrate the performance of this method under presenting the random censoring.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.159-169
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• 1993

In this article, we consider two sample problem with randomly right censored data. We propse two-sample confidence intervals for the difference in medians or any quantiles, based on bootstrap. The bootstrap version of two-sample confidence intervals proposed in this article is simple to apply and do not need the assumption of the shift model, so that for the non-shift model, the density estimation is not necessary, which is an attractive feature in small to moderate sized sample case.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.765-776
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• 2006

In this paper we propose an estimation method on the regression model with randomly censored observations of the training data set. The weighted least squares support vector machine regression is applied for the regression function estimation by incorporating the weights assessed upon each observation in the optimization problem. Numerical examples are given to show the performance of the proposed estimation method.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.917-927
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• 1997

Consider the confidence interval estimators of treatment effect when some of data to be analyzed are randomly censored, assuming two-sample location-shift model. Recently proposed PARK and PARK(1995) Estimators is discussed and a bootstrap estimator is proposed. This estimator is compared with other well-known estimators throught the simulation studies and recommendations about the use are made.

• The Mathematical Education
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• v.31 no.2
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• pp.133-140
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• 1992

The problem of estimating a smooth distribution function F at a point $\tau$ based on randomly right censored data is treated under certain smoothness conditions on F . The asymptotic performance of a certain class of kernel estimators is compared to that of the Kap lan-Meier estimator of F($\tau$). It is shown that the .elative deficiency of the Kaplan-Meier estimate. of F($\tau$) with respect to the appropriately chosen kernel type estimate. tends to infinity as the sample size n increases to infinity. Strong uniform consistency and the weak convergence of the normalized process are also proved.

• ETRI Journal
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• v.18 no.3
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• pp.207-213
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• 1996

This paper proposes a new nonparametric test for testing the null hypothesis that the MRL is constant against the alternative hypothesis that the MRL is decreasing (increasing) for ramdomly censored data. The proposed test statistic is a L-statistic, and we use L-statistic theory to establish its asymptotic normality of the test statistic. We discuss the efficiency loss due to censoring and also calculate the asymptotic relative efficiencies of our test statistic with respect to the Chen, Hollander and Langberg's test for several alternatives.