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Thus, assuming [A] and using Proposition 1, we may write

Figure 8 Thus, assuming [A] and using Proposition 1, we may write

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Assuming mild moment conditions on the sample distribution, our main result (Theorem 1) offers an asymptotic development of the form
Assuming mild moment conditions on the sample distribution, our main result (Theorem 1) offers an asymptotic development of the form
Hence, using identities (5)-(6), Theorem 1 takes the form
Hence, using identities (5)-(6), Theorem 1 takes the form
Solving this quadratic equation in 6,, we see that the right-hand side is uniformly minimized fo is an unbiased estimate of o. Besides, still assuming normality and letting (6,), be some generic positive normalization sequence, we may write
Solving this quadratic equation in 6,, we see that the right-hand side is uniformly minimized fo is an unbiased estimate of o. Besides, still assuming normality and letting (6,), be some generic positive normalization sequence, we may write
Proposition 1. Assume that Assumption [A] is satisfied. Then, as n — and observe that, by the central limit theorem and Slutsky’s lemma (van der Vaart [17, Chapter
Proposition 1. Assume that Assumption [A] is satisfied. Then, as n — and observe that, by the central limit theorem and Slutsky’s lemma (van der Vaart [17, Chapter
4.2. Proof of Theorem 1 Observe that Ss 1= Cro lon? where C, = By /Q, € (0,1) by assumption (7). Consequently, by Lemma
4.2. Proof of Theorem 1 Observe that Ss 1= Cro lon? where C, = By /Q, € (0,1) by assumption (7). Consequently, by Lemma
here C, + 0 as n — oo. Let B(x) be the cumulative distribution function of the standard normal stribution, that is, for all x € R,
here C, + 0 as n — oo. Let B(x) be the cumulative distribution function of the standard normal stribution, that is, for all x € R,
By assumption (i), we may write 62, = C,6),n, Where cy = Bn/ OQ, € (0,1). Consequently, by Lemma I,
By assumption (i), we may write 62, = C,6),n, Where cy = Bn/ OQ, € (0,1). Consequently, by Lemma I,
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