A Note on Convergence of Functions of Random Elements.
Abstract
Convergence of g(xi sub n) to g (xi) is considered when xi sub n approaches limit of xi distribution or in probability, without the usual restriction that g be continuous a.s. under the distribution of xi. It is shown that the covergence g (xi sub n) approaches limit of g (xi) holds for arbitrary Borel-measurable g, if in addition to the assumed convergence xi sub n approaches limit of xi the corresponding measures (p sub N) of (xi sub) are contiguous to the measure of P of xi in a certain very weak sense. Some statistical applications are indicated.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1985
- Accession Number
- ADA163405
Entities
People
- Robert J. Serfling
Organizations
- Johns Hopkins University