CORRELATION IN A BIVARIATE NORMAL DISTRIBUTION WHEN THE CONDITIONAL VARIANCES ARE KNOWN,

Abstract

This paper considers the problems of estimation and hypothesis testing for the correlation coefficient in a non-singular bivariate normal distribution when the conditional variances are known. Such problems arise, for example, when each of the variables can be measured by an instrument, with the other variable held fixed, and the instrument manufacturers specify the precision of the instrument. It is shown that the statistic of interest in this problem is the sample covariance, v. The distribution of v is derived, in addition to its moments, some properties, and its asymptotic behavior. Some percentage points of the null distribution are tabulated. It is shown that the distribution has the monotone likelihood ratio property in the correlation coefficient parameter, rho. Uniformly most powerful level alpha tests of rho are given, and the distribution of the maximum likelihood estimator of rho is developed. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1965
Accession Number
AD0469635

Entities

People

  • S. James Press

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Mathematics
  • Normal Distribution
  • Precision
  • Statistical Algorithms
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.