On estimating the mean in a bivariate normal distribution with equal or unequal variances

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Abstract

This paper considers the problem of estimating the mean μx of one of the components of the bivariate normal distribution with equal variances or unequal variances. When the mean of the other component μy is equal to μx, it is advantageous to pool the two sample means as an estimator of μx. When the experimenter is uncertain whether μx = μy, a preliminary test of significance is used at level α to test μx = μy. Three estimators of μx are considered, (i) preliminary test estimator (PTE), (ii) weighting function estimator (WFE), and (iii) adaptive preliminary test estimator (APTE). The WFE is defined as the linear combination of the two sample means with the weight obtained by minimizing the mean square error. The APTE is a PTE with the weight adopted from WFE. The biases, mean square errors, and relative efficiencies of all the three estimators are studied.

Original languageEnglish
Pages (from-to)155-170
Number of pages16
JournalJournal of Statistical Computation and Simulation
Volume58
Issue number2
DOIs
StatePublished - 1997

Keywords

  • Adaptive preliminary test estimator
  • Bias
  • Mean square error
  • Monte Carlo simulation
  • Optimal weight
  • Preliminary test estimator
  • Relative efficiency
  • Weighting function estimator

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