A Study on Applications of the Generalized Component Approach to the High-dimensional Equivalence Test of Means

• Main Authors: Ssu-Ming Chen, 陳斯明
• Other Authors: Jen-Pei liu
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/9a44ue

碩士 === 國立臺灣大學 === 農藝學研究所 === 105 === Traditionally, the Hotelling T2 test is applied to detect the difference in mean vectors between two populations. However for the high-dimensional data where the number of variables (p) is greater than the sample size (n), the inverse of the covariance matrix does not exist, and hence the Hotelling T2 statistic can not be calculated. Various methods were proposed to resolve this issue for the high-dimensional data. However these methods are to test the difference, not equivalence in mean vectors between two populations. The literature on the average equivalence in high-dimensional data is scarce. Chiu (2016) first applied a supremum-based method by Cai, et. al. (2014) to high-dimensional average equivalence problem. However, Chiu’s method depends upon only the variable with the largest difference and ignore the information provided from the rest of other variables. In this thesis, we proposed two equivalence tests for high-dimensional data. The first method, the General Component Equivalence Test (GCET) extended the procedure by Gregory (2015) to the high-dimensional average equivalence problem. Since the GCET is the average of squared t-statistics of p-variables, it ignores the directions of mean differences. To outcome this shortcoming, we further propose the Compound Covariate Equivalence Test (CCET). Extensive simulation studies were conducted under various conditions to investigate the performance on the size and power of the two proposed methods. Simulation results reveal that the CCET not only control the size at the nominal level but also can provide sufficient power. A numerical example illustrates applications of the proposed methods.