Generalized Simultaneous Confidence Region for Regression Coefficients and Their Ratio

• Main Authors: Wen-chun Chen, 陳玟君
• Other Authors: Tsai-yu Lin
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/65932114569714368986

碩士 === 逢甲大學 === 應用數學所 === 99 === Breeders are usually interested in inferences on the ratio along with the dominance and additive effects. This thesis considers the problem of finding simultaneous confidence region for two regression coefficients and their ratio of general linear models. We use the concept of generalized pivotal quantities to construct the simultaneous confidence region including Plug-in (II), Bonferroni correction and Generalized Variable approach. The proposed methods are compared with the two traditional methods, Worst-case and Plug-in (I), based on the multivariate-t distribution. A simulation study using the dominance ratio in crossing experiments with plants is computed from an estimate of the dominance and additive gene effects. Detailed statistical simulation studies are conducted to evaluate their performance by the coverage rate. Furthermore, some practical examples are given to illustrate the proposed procedures.