Importance sampling for simulations of moderate deviation probabilities of statistics

Large Deviation Principle for Moderate Deviation Probabilities of Bootstrap Empirical Measures

“…As have been shown in [15] and [16], MDP for empirical measures and technique of differentiation in functional spaces allow to establish MDP for differentiable statistical functionals. It turns out that this technique works to the same extent as in the proof of asymptotic normality [27].…”

“…be the rate function (in statistical terms, 2ρ 2 0 (G|P ) is the Fisher information) which arises naturally in the MDP analysis of empirical measuresP n (see [4]; [16], [2] and [15] ).…”

“…Theorem 3.3 provided below can be considered as a version of moderate deviation principle established in [2] for empirical processes. In such a form this MDP has been proved in [15] and is provided here for comparison with the bootstrap results. Define the set Ψ of measurable functions f :…”

“…In section 4 we discuss the extensions of these results on the case of differentiable statistical functionals. We show that the technique developed in [15] and [16] can be also implemented for the bootstrap setup. In particular MDP for the bootstrap empirical quantile processes and the bootstrap empirical copula functions are provided.…”

“…Probabilities of moderate deviations of statistics have been studied in numerous works (see [1,3,19,20] and references therein). Last time this problem was explored in terms of differentiable statistical functionals [15,16].…”