Let us outline the contents of the chapters to follows.

Chapter 2 concerns the problem of constructing simultaneous confidence interval for multinomial proportions. In this chapter, two alternative procedures are proposed. One of them is obtained by using the exact relation between binomial tail probabilities and tail probabilities of the F distribution. The other one is derived by using the power-divergence statistics introduced by Cressie and Read（1984） and Monte Carlo sampling technique. Numerical comparisons are then presented to evaluate these approaches and compare their performance with existing methods that have been used in statistical literature, and the main advantages of these new procedures are discussed finally.

In chapter 3, the emphasis shifts from interval estimation to multiple-hypothesis testing problem. In particular, we focus our discussion on a specific type of multiple tests which has a significant application in cytogenetics of one site with the others into consideration and can test the nonrandomness of breakpoints under either the proportional probability model or the equiprobability model are proposed. The first procedure is derived using the largest order statistic. The second procedure is developed form hierarchical-clustering viewpoint and is derived by using union-intersection principle. Hochberg’s（1988） algorithm, and Bohm et al’s（1995） stepwise testing procedure. To illustrate their real application, both of the two new procedures are applied to the detection of fragile sites for Chinese patients with colorectal carcinoma.

Summary of the previous chapters and areas where we believe future research would be rewarding are presented in chapter 4.

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