The Second-Order Bias and Mean Squared Error of Estimators in Time Series Models

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Joint Confidence Sets for Structural Impulse Responses (2016, unknown): “T 1 2 (γ(X̄T )− γ(μ)) = B0ZT + T− 1 2B1(ZT ⊗ ZT ) + · · ·+ T− H 2 BH(ZT ⊗ · · · ⊗ ZT ) + op(T H 2 ), (3)”
Toward Distribution Estimation under Local Differential Privacy with Small Samples (2018, methodology): “Note that this correction method was used to reduce the bias of the estimate [5, 41].”
Bias in the estimation of the mean reversion parameter in continuous time models (2012, methodology): “(1996),VinodandShenton (1996), MacKinnon and Smith (1998), and Bao and Ullah (2007). can be ignored when the mean reversion parameter is far away from zero.”
A general method for third-order bias and variance corrections on a nonlinear estimator (2015, methodology): “This is believed to be the reason for the incoherent Monte Carlo results of Bao and Ullah (2007a).”
Finite sample properties of maximum likelihood estimator in spatial models (2007, background): “(1996) and Bao and Ullah (2003) obtained the stochastic expansion in (4) except that they wrote cnðyÞ 1⁄4 Pn i1⁄41 qiðZi; yÞ=n and used Assumptions 4 and 6 in terms of qiðZi; yÞ.”