Nonparametric Tests Under Mixture Models

• Main Authors: Chen,Chien-Chang, 陳建彰
• Other Authors: Shen, Pao-Sheng
• Format: Others
• Language: en_US
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/72930083798275936280

碩士 === 東海大學 === 統計學系 === 86 === Under mixture models, the distribution function for lifetime Xi of an individual i drawn at random is F(x)=(1-PI)Fd(x) for x in [0, tau_f], where 0<=PI< 1 denotes the proportion of `immune' or `cured' individuals,Fd(x) denotes the distribution function of `susceptible' individuals with the right extreme tau_f. Assuming an independent censoring model, observations are of the formTi=min{Xi,Ci} (i=1,...,n), where Ci's are censoring times with right extreme tau_g and independent of Xi's.Assuming PI>0,they propose a nonparametric statistic to test H0:tau_f>=tau_g versus Ha:tau_f<tau_g.In this article, it is shown that under Ha the power of the test converges to 1. However, our investigation shows that the test is not able to control Type I error for testing the hypothesis of H0.It is pointed out that assuming tau_f<tau_g,the test is useful for testing the hypothesis of H0^:PI=0 versus Ha^:PI>0.