On the Variance of Probability Estimates with Correlated Data

Abstract

The foundations for probability estimation are presented for random processes in discrete time. The estimators considered are the empirical distribution function and the amplitude histogram and conditions are given for these to be unbiased and consistent. Expressions for the variance and covariance of these estimators are presented and the effect of correlations on these quantities is discussed and demonstrated numerically by simulations. A theorem establishes a monotonic relation between the variance and the correlation for Gaussian processes.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1982
Accession Number
ADA126336

Entities

People

  • Robert R. Beland

Tags

DTIC Thesaurus Topics

  • Air Force
  • Amplitude
  • Covariance
  • Data Science
  • Distribution Functions
  • Estimators
  • Gaussian Distributions
  • Gaussian Processes
  • Histograms
  • Information Science
  • Normal Distribution
  • Probability
  • Random Variables
  • Stationary Processes
  • Statistical Algorithms
  • Statistics
  • Stochastic Processes

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.