here \(\hat{\upsilon}_{m,n}\) is a consistent estimator of \(\upsilon(P,Q)\):
$$\upsilon(P,Q)=\frac{1}{\lambda}\frac{1}{4(F'(\theta))^2}+\frac{1}{1-\lambda}\frac{1}{4(G'(\theta))^2}$$
Choices of \(\hat{\upsilon}_{m,n}\) may include the kernel estimator of Devroye and Wagner (1980), the bootstrap estimator of Efron (1992), or the smoothed bootstrap  Hall et al. (1989) to list a few. For further details, see Chung and Romano (2013). Current implementation uses the bootstrap estimator of Efron (1992)          