Two-Stage And Sequential Interval Estimates Of Fixed-Width And Coverage Probaility

This thesis mainly investigate the problem of confidence intervals of prescribed precision (e.g.,the intervals' width ) and prescribed reliability controlled by coverage probability. Precision and reliability are two contradictory aspects of the theory of interval estimates. To find a confidence interval of prescribed width and prescribed probability is of groat importance in practical applications, arid thereby sequential procedures have to be employed in many cases.Here, Two topics: two-stage and pure sequential procedures are probed into. From finite to pure sequential steps, the two enrich sequential interval estimates by different means.When the family of distributions satisfy some conditions, the confidence intervals of prescribed width and prescribed coverage probability could be obtained by two-stage procedures. In chapter 1, the author first study the two-stage confidece intervals for the variance of a normal distribution, then work out the optimal sample size of the first stage by numerical computations and establish a proof for the non-existence of fixed-size sampling. Next, the author construct the two-stage confidece intervals for the parameters of the more general location and scale family. Further, the author discuss the correspondent problem in normal linear models, design Bonferroni, Scheffe and the maximum modulus t.two-stage confidence intervals respectively.Two-stage sampling has only one chance of using the information provided by samples to determine the following plan. Pure sequential sampling, however, could use sampling size sparingly. In addition, in some cases, pure sequential procedures have to be applied to acquire the confidence intervals which meet the demands. In chapter 2, first the author adopt pure sequential approach to gain cofidence bounds for linear regression parameters, which could be regarded as the continuations of the work of Gle.ser(1965). After that, the author focus his attention on the pure sequential confidence for the error variance in linear models. Finally, the pure sequential confidence for the quantilo are considered. This chapter has proved the sampling methods in above three cases are asymptotically consistent and asymptotically efficient as the width goes to zero.