CONVERGENCE RATES FOR WEIGHTED SUMS OF RANDOM VARIABLES.

Abstract

Let X sub 1, X sub 2, ... be independent random variables and let a sub (nk) be constants. Let S sub n = 1/n (Summation from k=1 to k=n of (X sub k - EX sub k)) and let A sub n = Summation from k=1 to k = infinity, of a sub (nk) (X sub k - EX sub k). The main purpose of this study was the investigation of the rate of convergence of P(absolute value of A sub n > epsilon) to zero under various assumptions on the X sub k's. In addition to the main results, results were obtained in ergodic theory, maximum likelihood estimation, testing against trend, and bidding theory. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 20, 1968
Accession Number
AD0669771

Entities

People

  • Charles R. Mann
  • David L. Hanson
  • F. T. Wright
  • H. D. Brunn
  • Maxwell Engelhardt

Organizations

  • University of Missouri

Tags

DTIC Thesaurus Topics

  • Convergence
  • Mathematics
  • Maximum Likelihood Estimation
  • Random Variables

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.