• Title, Summary, Keyword: Asymptotic variances

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Optimal Designs for Constant Stress Partially Accelerated Life Tests under Type I Censoring

  • Moon, Gyoung-Ae
    • Journal of the Korean Data and Information Science Society
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    • v.6 no.2
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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.

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Estimation for Autoregressive Models with GARCH(1,1) Error via Optimal Estimating Functions.

  • Kim, Sah-Myeong
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.1
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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.

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Sequential Estimation with $\beta$-Protection of the Difference of Two Normal Means When an Imprecision Function Is Variable

  • Kim, Sung-Lai;Kim, Sung-Kyun
    • Journal of the Korean Statistical Society
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    • v.31 no.3
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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.

Sequential Confidence Interval with $\beta$-protection for a Linear Function of Two Normal Means

  • Kim, Sung-Lai
    • Journal of the Korean Statistical Society
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    • v.26 no.3
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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.

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Asymptotic Relative Efficiencies of the Nonparametric Relative Risk Estimators for the Two Sample Proportional Hazard Model

  • Cho, Kil-Ho;Lee, In-Suk;Choi, Jeen-Kap;Jeong, Seong-Hwa;Choi, Dal-Woo
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.1
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    • pp.103-110
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    • 1999
  • In this paper, we summarize some relative risk estimators under the two sample model with proportional hazard and examine the relative efficiencies of the nonparametric estimators relative to the maximum likelihood estimator of a parametric survival function under random censoring model by comparing their asymptotic variances.

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A Bayesian Test Criterion for the Behrens-Firsher Problem

  • Kim, Hea-Jung
    • Communications for Statistical Applications and Methods
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    • v.6 no.1
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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.

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A New Redescending M-Estimating Function

  • Pak, Ro-Jin
    • Journal of the Korean Data and Information Science Society
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    • v.13 no.1
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    • pp.47-53
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    • 2002
  • A new redescending M-estimating function is introduced. The estimators by this new redescending function attain the same level of robustness as the existing redescending M-estimators, but have less asymptotic variances than others except few cases. We have focused on estimating a location parameter, but the method can be extended for a scale estimation.

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AMLE for Normal Distribution under Progressively Censored Samples

  • Kang, Suk-Bok;Cho, Young-Suk
    • Journal of the Korean Data and Information Science Society
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    • v.9 no.2
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    • pp.203-209
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    • 1998
  • By assuming a progressively censored sample, we propose the approximate maximum likelihood estimator (AMLE) of the location nd the scale parameters of the two-parameter normal distribution and obtain the asymptotic variances and covariance of the AMLEs. An example is given to illustrate the methods of estimation discussed in this paper.

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AMLE for the Rayleigh Distribution with Type-II Censoring

  • Kang, Suk-Bok;Cho, Young-Suk;Hwang, Kwang-Mo
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.2
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    • pp.405-413
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    • 1999
  • By assuming a type-II censoring, we propose the approximate maximum likelihood estimators (AMLEs) of the location and the scale parameters of the two-parameter Rayleigh distribution and calculate the asymptotic variances and covariance of the AMLEs.

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On the maximum likelihood estimation for a normal distribution under random censoring

  • Kim, Namhyun
    • Communications for Statistical Applications and Methods
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    • v.25 no.6
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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.