SOME STATISTICAL PROBLEMS CONNECTED WITH STOCHASTIC PROCESSES
Abstract
The statistical problem treated here is that of testing the hypothesis that a sample of n independent, identically distributed random variables have the common continuous distribution function F(x), specified in advance. In principle this will give confidence regions for the unknown distribution function, for if we have a test (based on the n observations) for every F(x), the confidence region will consist of precisely those F(x) for which the corresponding hypotheses are not rejected. For large n certain asymptotic tests are developed which were envisaged by Kolmogoroff, Smirnov, Cramer, and von Mises. The method used here is to reduce the problems down to more or less straightforward considerations in the theory of continuous Gaussian stochastic processes- a reduction developed by Doob, and used by him to give a simplified proof of Kolmogoroff's fundamental result. This note considers somewhat more refined questions which may be of interest to statisticians. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 11, 1949
- Accession Number
- AD0293676
Entities
People
- D.a. Darling
- T.w. Anderson
Organizations
- RAND Corporation