On the efficiency of BAN estimates of the parameters of normal populations based on singly censored samples
S. A. D. C. Doss · Biometrika · 1962
It is shown that the best asymptotically normal (BAN) estimates of the parameters (θ 1 , θ 2 , … θ k ) of a population f (x; θ 1 , θ 2 , …, θ k ) based on a censored sample of size N are jointly more efficient than those based on a truncated sample of size n , where n is the number of measured observations in the censored sample. In the case of normal populations it is established that, both when the mean μ and the standard deviation σ are jointly estimated and when μ alone is estimated σ being known, the BAN estimates of the parameters based on a censored sample of size N are more efficient than those based on a complete sample of size n , where n is the number of measured observations in the censored sample. However, when we are estimating σ alone μ being known, this result is true only when the point of truncation x α is above μ. In the other case, when x α is below μ, the BAN estimate of σ based on the censored sample is less efficient than that based on the complete sample. Throughout the paper, in the case of joint estimation, Joint efficiency is taken as the criterion.