Essays in Honor of Cheng Hsiao by Terrell Dek;Li Tong;Pesaran M. Hashem;

Author:Terrell, Dek;Li, Tong;Pesaran, M. Hashem;
Language: eng
Format: epub
Publisher: Emerald Publishing Limited
Published: 2020-01-25T00:00:00+00:00

In the case when 1 < α < 2, we have Bn ≈ K(n/kn)1/α−1 for some constant K. Hence, the ratio of the bias and standard deviation is given by

which tends to infinity as n → ∞. This implies that the bias Bn dominates the distribution of asymptotically. Consequently, it is vital to correct for this bias. In the next section, we consider a bias-corrected version of the tail-trimmed estimator.

2.3. Bias-corrected Tail-trimmed Estimator

In this section, we introduce the bias-corrected tail-trimmed estimator and show that it is asymptotically normal. To that end, we need to restrict the tails of the importance sampling estimator to satisfy Assumption 1 instead of Assumption 1′ – the former is needed to establish the convergence rate of .

It follows from (6) that a natural estimator for the bias is:

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