• Journal of the Korean Data and Information Science Society
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• 제6권2호
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• pp.77-83
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• 1995

The inferences on a series system under the usual condition using data from constant stress partially accelerated life tests and type I censoring is studied. Two optimal designs to determine the sample proportion allocated each stress level model are also presented, which minimize the sum of the generalized asymptotic variances of maximum likelihood estimators of the failure rate and the acceleration factors and the sum of the asymptotic variances of maximum likelihood estimators of the acceleration factors for each component. Each component of a system is assumed to follow an exponenial distribution.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.207-214
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• 1999

Optimal estimating functions for a class of autoregressive models with GARCH(1,1) error are discussed. The asymptotic properties of the estimator as the solution of the optimal estimating equation are investigated for the models. We have also some simulation results which suggest that the proposed optimal estimators have smaller sample variances than those of the Conditional least-squares estimators under the heavy-tailed error distributions.

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.193-205
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• 1999

An approximate Bayes criterion for Behrens-Fisher problem (testing equality of means of two normal populations with unequal variances) is proposed and examined. Development of the criterion involves derivation of approximate Bayes factor using the imaginary training sample approachintroduced by Spiegelhalter and Smith (1982). The proposed criterion is designed to develop a Bayesian test criterion having a closed form, so that it provides an alternative test to those based upon asymptotic sampling theory (such as Welch's t test). For the suggested Bayes criterion, numerical study gives comparisons with a couple of asymptotic classical test criteria.

• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.309-317
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• 1997

A sequential procedure for estimating a linear function of two normal means which satisfies the two requirements, i.e. one is a condition of coverage probability, the other is a condition of $\beta$-protection, is proposed when the variances are unknown and not necessarily equal. We give asymptotic behaviors of the proposed stopping time.

• Journal of the Korean Statistical Society
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• 제31권3호
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• pp.379-389
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• 2002

For two normal distribution with unknown means and unknown variances, a sequential procedure for estimating the difference of two normal means which satisfies both the coverage probability condition and the $\beta$-protection is proposed under some smoothness of variable imprecision function, and the asymptotic normality of the proposed stopping time after some centering and scaling is given.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.115-134
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• 1994

Polynomial errors-in-variables model with one predictor variable and one response variable is defined and an estimator of model is derived following the Booth's linear model estimation procedure. Since polynomial model is nonlinear function of the unknown regression coefficients and error-free predictors, it is nonlinear model in errors-in-variables model. As a result of applying linear model estimation method to nonlinear model, some additional assumptions are necessary. Hence, an estimator is derived under the assumption that the error variances are decrasing as sample size increases. Asymptotic propoerties of the derived estimator are provided. A simulation study is presented to compare the small sample properties of the derived estimator with those of OLS estimator.

• Communications for Statistical Applications and Methods
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• 제21권6호
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• pp.529-538
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• 2014

In this paper, we consider maximum likelihood estimators of normal distribution based on type II censoring. Gupta (1952) and Cohen (1959, 1961) required a table for an auxiliary function to compute since they did not have an explicit form; however, we derive an explicit form for the estimators using a method to approximate the likelihood function. The derived estimators are a special case of Balakrishnan et al. (2003). We compare the estimators with the Gupta's linear estimators through simulation. Gupta's linear estimators are unbiased and easily calculated; subsequently, the proposed estimators have better performance for mean squared errors and variances, although they show bigger biases especially when the ratio of the complete data is small.

• Communications for Statistical Applications and Methods
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• 제25권6호
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• pp.647-658
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• 2018

In this paper, we study statistical inferences on the maximum likelihood estimation of a normal distribution when data are randomly censored. Likelihood equations are derived assuming that the censoring distribution does not involve any parameters of interest. The maximum likelihood estimators (MLEs) of the censored normal distribution do not have an explicit form, and it should be solved in an iterative way. We consider a simple method to derive an explicit form of the approximate MLEs with no iterations by expanding the nonlinear parts of the likelihood equations in Taylor series around some suitable points. The points are closely related to Kaplan-Meier estimators. By using the same method, the observed Fisher information is also approximated to obtain asymptotic variances of the estimators. An illustrative example is presented, and a simulation study is conducted to compare the performances of the estimators. In addition to their explicit form, the approximate MLEs are as efficient as the MLEs in terms of variances.

• 품질경영학회지
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• 제21권2호
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• pp.162-169
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• 1993

For the problem of testing the parallelism of several regression lines against ordered alternatives, two test statistics and proposed and examined. The proposed statistics are linear combinations of robust estimators of slope parameters, which are modifications of the Adichie (1976) test based on scores. The asymptotic null variances of the proposed states tics are estimated by the kernel density estimation methods. The proposed tests are compared with the Adichie's test in terms of asymptotic relative efficiency and small-sample powers.

• 응용통계연구
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• 제9권1호
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• pp.53-73
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• 1996

일정형 및 계단형 가속수명시험의 시험설계에 대한 일반적인 모형과 최적설계에 대한 최근의 연구결과를 소개하고, 수명분포가 와이블인 경우에 대하여 두가지 시험방법에 대한 최적설계를 점근분산의 행태, 설계변수의 효과, 최적시험조건에서 시험종결 시점까지의 기대고장개수 및 기대시험종결시간, 점근분산의 상대적효율과 설계변수의 사전추정치에 대한 둔감성의 측면에서 비교, 분석하였다.