Delta Method, Infinite Dimensional

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Inference for empirical Wasserstein distances on finite spaces (2016, methodology): “Theorem 3 (Römisch (2004), theorem 1).”
Statistical estimation of composite risk functionals and risk optimization problems (2015, methodology): “Therefore, we can apply the delta method (see, Römisch 2006) to infer that √ n ( v(h(n)) − v(h̄)) D−→ min z∈S(h̄) Φ ′h(z, h̄)W. Substituting the functional form of Φ, we obtain Φ ′h(z, h̄) = ∇ f1 ( z,E[ f2(z, X)] ) δz, where δz is the Dirac measure at z. Application of this operator to the processW…”
Empirical optimal transport on countable metric spaces: Distributional limits and statistical applications (2017, methodology): “A.1 Hadamard directional differentiability In this section we follow mainly Shapiro (1991) and Römisch (2004).”
Survival Analysis With Quantile Regression Models (2008, unknown): “Applying the Taylor expansion technique to κ[μ{β̂(τ )}] − κ[μ{β0(τ )}] and the continuous mapping theorem, we get that for τ ∈ [ν, τU ], n1/2{β̂(τ ) − β0(τ )} converges weakly to B{β0(τ )}−1φ{G(τ )}, which also is Gaussian.”
Optimal-order bounds on the rate of convergence to normality in the multivariate delta method (2009, methodology): “The reader is referred to [75] for a rather detailed description of the delta method and its applications; see [39, 71] for a more modern treatment of the delta method applied to infinite-dimensional random vectors.”