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        Modified Broemeling's Method Confidence Intervals for the Ratio(C) of Total Variance in Two-Factor Nested Variance Components Model

        강관중,김민규,김흔창 한국자료분석학회 2014 Journal of the Korean Data Analysis Society Vol.16 No.3

        The confidence intervals for sigma_C^2 / ( sigma_A^2 + sigma_B^2 + sigma_C^2 ) are given in various forms by many authors in two-factor nested variance components model Y_ijk = mu + A_i +B_ij + C_ijk. In this model, we can find out the confidence intervals for sigma_B^2 / sigma_C^2 by using Broemeling's method of the confidence intervals for sigma_A^2 / sigma_C^2 and sigma_A^2 / sigma_B^2. And we can find out a confidence intervals for sigma_C^2 / ( sigma_A^2 + sigma_B^2 + sigma_C^2 ) by using those of the confidence intervals for sigma_A^2 / sigma_C^2, sigma_A^2 / sigma_B^2 and sigma_B^2 / sigma_C^2. Then, by the simulation results of this confidence intervals for sigma_C^2 / ( sigma_A^2 + sigma_B^2 + sigma_C^2 ) are not fit exactly for 100(1-alpha)% confidence intervals and the ranges of width are wide. Then the confidence intervals are close to 100(1-alpha)% when K is large number from 1,000 to 1,000,000. But this K is too large to use for estimation and test. Thus, we give a new modified confidence intervals for sigma_C^2 / ( sigma_A^2 + sigma_B^2 + sigma_C^2 ) in this model. The simulation results show that the modified confidence intervals are better than those obtained by using Broemeling's method of the confidence intervals, and we can use for estimation and test.

      • KCI등재

        Modified Wang's Method Confidence Intervals for the Ratio(C) of Total Variance in Two-Factor Nested Variance Components Model

        강관중,김민규,김흔창,김가영 한국자료분석학회 2014 Journal of the Korean Data Analysis Society Vol.16 No.5

        The confidence intervals for sigma_C^2 / ( sigma_A^2 + sigma_B^2 + sigma_C^2 ) are given in various forms by many authors in two-factor nested variance components model Y_ijk = mu + A_i + B_ij + C_ijk. In this model, similar to the method of Kang (2014), we can find out the confidence intervals for sigma_B^2 / sigma_C^2 by using Wang’s method of the confidence intervals for sigma_A^2 / sigma_C^2 and sigma_A^2 / sigma_B^2. And we can find out a confidence intervals for sigma_C^2 / ( sigma_A^2 + sigma_B^2 + sigma_C^2 ) by using those of the confidence intervals for sigma_A^2 / sigma_C^2, sigma_A^2 / sigma_B^2 and sigma_B^2 / sigma_C^2. Then, by the simulation results of this confidence intervals for sigma_C^2 / ( sigma_A^2 + sigma_B^2 + sigma_C^2 ) are not fit exactly for 100(1-alpha)% confidence intervals and the ranges of width are wide. Then the confidence intervals are close to 100(1-alpha)% when K is large number from 1,000 to 1,000,000. But this K is too large to use for estimation and test. Thus, we give a new modified confidence intervals for sigma_C^2 / ( sigma_A ^2 + sigma_B^2 + sigma_C^2 ) in this model. The simulation results show that the modified confidence intervals are better than those obtained by using Wang’s method of the confidence intervals, and we can use for estimation and test.

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