Positivity of the best unbiased \(L\)-estimator of the scale parameter with complete or selected order statistics from location-scale distribution. (English) Zbl 1003.62511
Summary: The positivity of the best linear unbiased estimator of the scale parameter of a location-scale family of distributions in terms of complete or selected set of order statistics has only been conjectured in the literature based solely on empirical evidence. This paper offers an analytical proof of this conjecture for distributions whose densities are log-concave.
MSC:
| 62G05 | Nonparametric estimation |
| 62F10 | Point estimation |
| 62G30 | Order statistics; empirical distribution functions |
References:
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