TY  - CHAP
AB  - Abstract When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is twofold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk.
VL  - 33
SN  - 978-1-78441-183-1/0731-9053
DO  - 10.1108/S0731-905320140000033015
UR  - https://doi.org/10.1108/S0731-905320140000033015
AU  - Song Kyungchul
PY  - 2014
Y1  - 2014/01/01
TI  - Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk
T2  - Essays in Honor of Peter C. B. Phillips
T3  - Advances in Econometrics
PB  - Emerald Group Publishing Limited
SP  - 557
EP  - 585
Y2  - 2024/04/16
ER  -