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SUMMARY Suppose we have a random sample of size n from a distribution with parameters (p l, …,pk) Then, for large n, if (p 1,…, pk) satisfy any model ω of dimension less than k, any function of (p 1, …, pk) can be estimated more precisely by using this model than by using the general model with all k parameters. This result will not be at all surprising to experienced statisticians, but a formal statement and proof of it should be useful in teaching prospective statisticians.
P. M. E. Altham (Sat,) studied this question.