Evaluate and compare the transformation of T-statistic with skewed data

• Main Authors: kuan-Wen Su, 蘇貫文
• Other Authors: Ying-Chieh Yeh
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/d7cp4k

碩士 === 國立中央大學 === 工業管理研究所 === 105 === When we are trying to construct a confidence interval with small sample size, we can use t-statistic construct the(1-α)100%confidence interval to evaluate the population mean if the data is independent and identical from normal distribution. If data comes from a skewed distribution, the coverage accuracy of t-statistic is poor. In order to solve this problem, Hall (1992) proposed the modified t-statistic to remove the effect of skewness and Zhou (2005) proposed a new t-statistic which he claim the new statistic can get shorter confidence interval length than Hall’s t-statistic. Zhou’s comparison is based on traditional criterion; it has some contradiction when we use it to measure the CIP is good or not (i.e. when we want a tighter confidence width, we will get less coverage probability, vice versa. We will use a new criterion to evaluate the CIP build by these authors, which proposed by Yeh and Schemeiser (2015) called VAMP1RE Criterion. The new Criterion is based on the coverage value which is proposed by Schruben (1980). VAMP1RE Criterion can be decomposing into two causes, Departure form Validity and Inability to mimic. VAMP1RE Criterion can be find by the coverage value of Ideal CIP and proposed CIP then calculate the mean-squared error of the two coverage value. We will use VAMP1RE Criterion to compare the t-statistic proposed by Zhou (2005)、Hall (1992) and Johnson (1978).