Saddlepoint Approximation to the distribution of Correlation Coefficient

• Main Authors: Yen-Jung Lien, 連晏榮
• Other Authors: Tai-Fang Chen
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/61558055022494563378

碩士 === 靜宜大學 === 應用數學研究所 === 96 === The sample correlation coefficient, R, is an important measurement in statistics. Since the distribution of R can not be expressed as a simple form, it is difficult to conduct any interval estimation. The Fisher-transformation is usually used as a tool for statistical inference. In this study, we derive saddlepoint approximations for the distribution of R with both Normal base and Beta base, and compare them with Fisher-transformation and Beta approximation methods. For different sample sizes, with specified values of ρ , the values of the CDF are calculated. Then these methods were critically evaluated according to the relative errors to the empirical distribution. In summary, there is no significant difference between Normal base and Beta base for the saddlepoint approximation. Beta approximation is the most accurate method among these methods for small samples, and both saddlepoint approximations show the best behavior for larger samples. Fisher-transformation acts well around both ends, but it gives a higher value around the center.