| Summary: | 碩士 === 靜宜大學 === 應用數學研究所 === 92 === For a random effect model in the experimental design, an exact confidence interval on a variance component usually cannot be obtained, so an approximation has to be used. One of the useful procedures is the modified large-sample(MLS) method. The confidence coefficients of this method are not good enough when the sample size is small or a one-tailed problem is considered. Therefore, for the case of small samples, two new methods were proposed to get a confidence lower limit for a nonnegative linear combination of two variance components, . These methods are trial-and-error method and functional method. The lower confidence limit given by either method had a special form as , where and are the unbiased minimum variance estimators of and respectively, and . The g-function for the trial-and-error method was obtained by manually adjusting the error, resulting in an error within 0.05%. The g-function for the functional method was obtained by using a numerical technique which minimize the sum of the square errors, resulting in an error within 1.78%. The value of the desired g-function can be easily obtained according to the graphics or the tables presented in this thesis, then the lower confidence limit for will be found.
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