12,186 research outputs found
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
Reducing variance in univariate smoothing
A variance reduction technique in nonparametric smoothing is proposed: at
each point of estimation, form a linear combination of a preliminary estimator
evaluated at nearby points with the coefficients specified so that the
asymptotic bias remains unchanged. The nearby points are chosen to maximize the
variance reduction. We study in detail the case of univariate local linear
regression. While the new estimator retains many advantages of the local linear
estimator, it has appealing asymptotic relative efficiencies. Bandwidth
selection rules are available by a simple constant factor adjustment of those
for local linear estimation. A simulation study indicates that the finite
sample relative efficiency often matches the asymptotic relative efficiency for
moderate sample sizes. This technique is very general and has a wide range of
applications.Comment: Published at http://dx.doi.org/10.1214/009053606000001398 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Adolescent precursors of early union formation among Asian American and Whites
This study investigates the relatively low rates of early marriage and cohabitation among Asian Americans compared to Whites. With an emphasis on family value socialization and other precursors measured in adolescence, data from Waves 1 and 3 of Add Health are used to test five hypotheses. Analyses of early marriage indicate that the Asian-White difference is driven primarily by differences in adolescent sexual and romantic relationship experiences, and several measures of family values play a stronger role among Asian Americans than Whites. Asian-White differences in cohabitation persist net of SES and other adolescent precursors, but differences are attenuated when parental value socialization, intimate relationship experiences, and educational investments are controlled. These results are interpreted within a culturally sensitive conceptual framework that emphasizes independent versus interdependent construals of the self.America
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