Asymmetric Kernel Smoothing by Masayuki Hirukawa

Author:Masayuki Hirukawa
Language: eng
Format: epub, pdf
Publisher: Springer Singapore, Singapore

The bias and variance approximations of the JLN-MBC estimator are documented in the next theorem.

Theorem 3.3

(Hirukawa 2010, Theorem 2; Hirukawa and Sakudo 2014, Theorem 2; Hirukawa and Sakudo 2015, Theorem 3)

If Assumptions 3.1 and 3.2 and hold, then the bias of can be approximated as

where can be obtained by replacing in given in Table 2.​1 with . In addition, regardless of the position of x.

JLN-MBC is yet another method that can improve the bias convergence from to . The expression in the leading bias coefficient looks complex at first glance. It should read as follows: for example, if we consider the case of the MG kernel again, then

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