A uniqueness result for L-estimators, with applications to L-moments

We show that if a linear combination of expectations of order statistics has mean zero across all random variables that have finite mean, then the linear combination is identically zero. A consequence of this result is that any functional of a probability distribution can have essentially only one unbiased L-estimator (i.e., an estimator that has the form of a linear combination of order statistics): if two such linear combinations have the …