1,335 research outputs found
Achieving Efficiency in Black Box Simulation of Distribution Tails with Self-structuring Importance Samplers
Motivated by the increasing adoption of models which facilitate greater
automation in risk management and decision-making, this paper presents a novel
Importance Sampling (IS) scheme for measuring distribution tails of objectives
modelled with enabling tools such as feature-based decision rules, mixed
integer linear programs, deep neural networks, etc. Conventional efficient IS
approaches suffer from feasibility and scalability concerns due to the need to
intricately tailor the sampler to the underlying probability distribution and
the objective. This challenge is overcome in the proposed black-box scheme by
automating the selection of an effective IS distribution with a transformation
that implicitly learns and replicates the concentration properties observed in
less rare samples. This novel approach is guided by a large deviations
principle that brings out the phenomenon of self-similarity of optimal IS
distributions. The proposed sampler is the first to attain asymptotically
optimal variance reduction across a spectrum of multivariate distributions
despite being oblivious to the underlying structure. The large deviations
principle additionally results in new distribution tail asymptotics capable of
yielding operational insights. The applicability is illustrated by considering
product distribution networks and portfolio credit risk models informed by
neural networks as examples.Comment: 51 page
Confidence Corridors for Multivariate Generalized Quantile Regression
We focus on the construction of confidence corridors for multivariate
nonparametric generalized quantile regression functions. This construction is
based on asymptotic results for the maximal deviation between a suitable
nonparametric estimator and the true function of interest which follow after a
series of approximation steps including a Bahadur representation, a new strong
approximation theorem and exponential tail inequalities for Gaussian random
fields. As a byproduct we also obtain confidence corridors for the regression
function in the classical mean regression. In order to deal with the problem of
slowly decreasing error in coverage probability of the asymptotic confidence
corridors, which results in meager coverage for small sample sizes, a simple
bootstrap procedure is designed based on the leading term of the Bahadur
representation. The finite sample properties of both procedures are
investigated by means of a simulation study and it is demonstrated that the
bootstrap procedure considerably outperforms the asymptotic bands in terms of
coverage accuracy. Finally, the bootstrap confidence corridors are used to
study the efficacy of the National Supported Work Demonstration, which is a
randomized employment enhancement program launched in the 1970s. This article
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