15,904 research outputs found
Bias of the Quasi Score Estimator of a Measurement Error Model Under Misspecification of the Regressor Distribution
In a structural error model the structural quasi score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification the true model consists of a mixture of normal distributions which cluster round a single normal distribution, in the second type the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero very fast so that small deviations from the true model lead only to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model
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
Polyelectrolyte Adsorption on Charged Substrate
The behavior of a polyelectrolyte adsorbed on a charged substrate of
high-dielectric constant is studied by both Monte-Carlo simulation and
analytical methods. It is found that in a low enough ionic strength medium, the
adsorption transition is first-order where the substrate surface charge still
keeps repulsive. The monomer density at the adsorbed surface is identified as
the order parameter. It follows a linear relation with substrate surface charge
density because of the electrostatic boundary condition at the charged surface.
During the transition, the adsorption layer thickness remains finite. A new
scaling law for the layer thickness is derived and verified by simulation.Comment: Proceedings of the 3rd Symposium on Slow Dynamics in Complex Systems,
3-8 November 2003, Sendai, Japa
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