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1The class of all possible consistent estimates of a given parameter c is very extensive and it includes a number of particular practically important estimates thoroughly studied in many statistical texts (see, e.g., Cramér, 1946; Wilks, 1962; Kendall and Stuart, 1966; Silvey, 1970; Zacks, 1971). To compare two different unbiased consistent estimators of c, say, C *N and C **N , the relative efficiency er(C **N , C *N ) or C **N as compared with C *N is sometimes evaluated by the formula er(C **N ,C *N ) = σ2(C *N )/σ2(C **N ). Clearly, C **N is preferable to C *N if, and only if, er(C **N C *N ) > 1. Note also that under some general conditions the lower bound σ 2N (c) to the variance σ2(C *N ) of any unbiased estimator C *N of a parameter c can be determined, and hence the absolute efficiency e(C *N ) = σ2(C *N )/σ *N (c) of C *N can be evaluated. The estimator C *N (and the estimate c *N ) is called efficient if e(C *N ) = 1 and asymptotically efficient if e(C *N ) → 1 as N → ∞.

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© 1987 Springer-Verlag New York Inc.

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Yaglom, A.M. (1987). Chapter 3. In: Correlation Theory of Stationary and Related Random Functions. Springer Series in Statistics. Springer, New York, NY.

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  • Print ISBN: 978-1-4612-9090-2

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