Approximating the Level Probabilities in Order Restricted Inference: The Simple Tree Ordering.

Abstract

Distribution theory for the likelihood ratio statistics for the comparison of several treatments with a control is discussed. These test statistics account for prior information that the treatments are at least as effective as the control. Their null distributions are mixtures of chi-squared or beta distributions and the mixing coefficients, which are level probabilities, are intractable for even a moderate number of treatments and unequal weights, which are typically the sample sizes. The distribution corresponding to equal weights is considered as an approximation and an approximation based on the pattern of large and small weights is developed. Both are adequate for moderate variations in the weights, but the approximation based on patterns in the weight set is considerably more accurate for larger variations. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1984
Accession Number
ADA140684

Entities

People

  • F. T. Wright
  • Tuan T. Tran

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Data Science
  • Discrete Distribution
  • Distribution Theory
  • Errors
  • Frequency
  • Information Science
  • Mathematics
  • Military Research
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistical Inference
  • Statistical Tests
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms