ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 62, 60 Różański, Roman, Wrocław University of Technology, Wrocław, Poland Asymptotically consistent and efficient fixed-size sequential confidence sets . A sequential confidence set based on an estimation process of a multivariate parameteris constructed. Under the assumption that the estimation process scaled by an increasing positive process has an asymptotic distribution it is proved that the sequential confidence set is asymptotically consistent and efficient. The results obtained are applied to the sequential confidence estimation in the exponential class of processes and for the estimation of the intensity function in the point process multiplicative model. A bootstrap fixed-size sequential confidence interval is also defined which is proved to be asymptotically consistent. Examples of application in nonparametric estimation for time series are given. Reference: R. Różański, The asymptotic consistency and efficiency of fixed-size sequential confidence sets, to appear in PMS.