2,736 research outputs found
Importance Sampling and its Optimality for Stochastic Simulation Models
We consider the problem of estimating an expected outcome from a stochastic
simulation model. Our goal is to develop a theoretical framework on importance
sampling for such estimation. By investigating the variance of an importance
sampling estimator, we propose a two-stage procedure that involves a regression
stage and a sampling stage to construct the final estimator. We introduce a
parametric and a nonparametric regression estimator in the first stage and
study how the allocation between the two stages affects the performance of the
final estimator. We analyze the variance reduction rates and derive oracle
properties of both methods. We evaluate the empirical performances of the
methods using two numerical examples and a case study on wind turbine
reliability evaluation.Comment: 37 pages, 6 figures, 2 tables. Accepted to the Electronic Journal of
Statistic
Nonparametric Inference via Bootstrapping the Debiased Estimator
In this paper, we propose to construct confidence bands by bootstrapping the
debiased kernel density estimator (for density estimation) and the debiased
local polynomial regression estimator (for regression analysis). The idea of
using a debiased estimator was recently employed by Calonico et al. (2018b) to
construct a confidence interval of the density function (and regression
function) at a given point by explicitly estimating stochastic variations. We
extend their ideas of using the debiased estimator and further propose a
bootstrap approach for constructing simultaneous confidence bands. This
modified method has an advantage that we can easily choose the smoothing
bandwidth from conventional bandwidth selectors and the confidence band will be
asymptotically valid. We prove the validity of the bootstrap confidence band
and generalize it to density level sets and inverse regression problems.
Simulation studies confirm the validity of the proposed confidence bands/sets.
We apply our approach to an Astronomy dataset to show its applicabilityComment: Accepted to the Electronic Journal of Statistics. 64 pages, 6 tables,
11 figure
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