  When a parameter of interest is defined to be a nondifferentiable transform
of a regular parameter, the parameter does not have an influence function,
rendering the existing theory of semiparametric efficient estimation
inapplicable. However, when the nondifferentiable transform is a known
composite map of a continuous piecewise linear map with a single kink point and
a translation-scale equivariant map, this paper demonstrates that it is
possible to define a notion of asymptotic optimality of an estimator as an
extension of the classical local asymptotic minimax estimation. This paper
establishes a local asymptotic risk bound and proposes a general method to
construct a local asymptotic minimax decision.
