Abstract In this thesis we propose a new methodology pute the critical values of using the Likelihood Ratio Test (LRT) on tubular models through Bootstrap simulation. We implement a Fast Double Bootstrap (FDB ) method to improve the reliability of critical values, and to evaluate the consistency of the Bootstrap, a triple-level Bootstrap simulation procedure is proposed and the direction selection technique is used to reduce plexity in the Bootstrap algorithm. Firstly, we develop testing procedures for the tubular hypothesis. The LRT statistic L2 is proposed as the test statistic and an iterative algorithm of computation is developed. The limiting distribution of the LRT statistic is used to construct the asymptotic critical value of the LRT statistic. Secondly, we apply the tubular testing method to data in a two-way table when model is row-column independent. The testing index rˆ* pared with other goodness-of-fit statistics, The LRT statistics are calculated for tubes with different tolerance radius. A semiparametric Bootstrap method is used to simulate the distribution 2nL2 of the LRT statistic, then pare the asymptotic distribution with the distribution obtained by Bootstrap simulation. We show how setting the critical value using Bootstrap testing results in rather substantial cha nges in r * inference in moderate sample sizes. We briefly discuss the possible reason for this difference. Lastly, we address whether the Bootstrap test achieves the right size reliably. This evaluation involves three levels of simulation. We develop an efficient procedure using direction selection and find that Bootstrap testing is satisfyingly accurate in size, and just a bit conservative. Keywords: Bootstrap, tubular model, likelihood ratio test, goodness of fit test 目 录 摘 要..........................................................................................................................I Abstract....................................................
