Effect of sample size on sampling properties of MLEs

Sample sizeMean (Embedded Image )SD (Embedded Image )θ in C.I.Embedded Image Embedded Image ρ in C.I.Embedded Image Embedded Image ρ/θ in C.I.
  • Shown are estimated means and standard deviations of the maximum-likelihood estimates of θ; estimated median of maximum-likelihood estimates of ρ and ρ/θ; g, the proportion of times that the MLE is within a factor of 2 of the truth; and coverage properties of an ~95% confidence interval (calculated using a chi-square approximation to the likelihood ratio statistic). Results are based on 100 samples (simulated with ρ = θ = 1.0) for each of three sample sizes.