Optimal Universal Coding and Density Estimation.

Abstract

Research progress has been made in the areas of empirical processes for mixing sequences, information theory, minimax estimation theory in source coding and nonparametric statistics, and Markov chain Monte Carlo (MCMC) methods. Rates of convergence and Central Limit Theorems results have been obtained for empirical processes of dependent data, and they are very useful for studying statistical models with dependence structure. On the important MCMC convergence diagnostic problem, regeneration points have been introduced into the Markov chain using the split-chain technique; so has been a global approach based on the the estimated L1 error and the Cusum path plot. Making connections between information theory and statistics, we obtained an information-theoretic result on the rate of convergence of a D-semifaithful code, and we also introduced non-parametric minimax lower bound techniques into bounding from below the redundancy in source coding. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Nov 28, 1994
Accession Number
ADA290694

Entities

People

  • Bin Yu

Organizations

  • University of Wisconsin Madison Department of Statistics

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Convergence
  • Data Science
  • Decision Theory
  • Estimators
  • Information Science
  • Information Theory
  • Markov Chains
  • Monte Carlo Method
  • Nonparametric Statistics
  • Probability
  • Sampling
  • Scientists
  • Sequences
  • Statistical Decision Theory
  • Statistics
  • Theorems

Readers

  • Computer Programming and Software Development.
  • Mathematical Modeling and Probability Theory.
  • Statistical inference.