54,240 research outputs found
boosting in kernel regression
In this paper, we investigate the theoretical and empirical properties of
boosting with kernel regression estimates as weak learners. We show that
each step of boosting reduces the bias of the estimate by two orders of
magnitude, while it does not deteriorate the order of the variance. We
illustrate the theoretical findings by some simulated examples. Also, we
demonstrate that boosting is superior to the use of higher-order kernels,
which is a well-known method of reducing the bias of the kernel estimate.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ160 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Flexible generalized varying coefficient regression models
This paper studies a very flexible model that can be used widely to analyze
the relation between a response and multiple covariates. The model is
nonparametric, yet renders easy interpretation for the effects of the
covariates. The model accommodates both continuous and discrete random
variables for the response and covariates. It is quite flexible to cover the
generalized varying coefficient models and the generalized additive models as
special cases. Under a weak condition we give a general theorem that the
problem of estimating the multivariate mean function is equivalent to that of
estimating its univariate component functions. We discuss implications of the
theorem for sieve and penalized least squares estimators, and then investigate
the outcomes in full details for a kernel-type estimator. The kernel estimator
is given as a solution of a system of nonlinear integral equations. We provide
an iterative algorithm to solve the system of equations and discuss the
theoretical properties of the estimator and the algorithm. Finally, we give
simulation results.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1026 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues
Bootstrap methods are widely used for distribution estimation, although in
some problems they are applicable only with difficulty. A case in point is that
of estimating the distributions of eigenvalue estimators, or of functions of
those estimators, when one or more of the true eigenvalues are tied. The
-out-of- bootstrap can be used to deal with problems of this general
type, but it is very sensitive to the choice of . In this paper we propose a
new approach, where a tie diagnostic is used to determine the locations of
ties, and parameter estimates are adjusted accordingly. Our tie diagnostic is
governed by a probability level, , which in principle is an analogue of
in the -out-of- bootstrap. However, the tie-respecting bootstrap
(TRB) is remarkably robust against the choice of . This makes the TRB
significantly more attractive than the -out-of- bootstrap, where the
value of has substantial influence on the final result. The TRB can be used
very generally; for example, to test hypotheses about, or construct confidence
regions for, the proportion of variability explained by a set of principal
components. It is suitable for both finite-dimensional data and functional
data.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ154 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Tunneling into fractional quantum Hall liquids
Motivated by the recent experiment by Grayson et.al., we investigate a
non-ohmic current-voltage characteristics for the tunneling into fractional
quantum Hall liquids. We give a possible explanation for the experiment in
terms of the chiral Tomonaga-Luttinger liquid theory. We study the interaction
between the charge and neutral modes, and found that the leading order
correction to the exponent is of the order of
, which reduces the exponent . We
suggest that it could explain the systematic discrepancy between the observed
exponents and the exact dependence.Comment: Latex, 5 page
Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise
correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho
and the spatial dimension d. By means of a stochastic Cole-Hopf transformation,
the critical and correction-to-scaling exponents at the roughening transition
are determined to all orders in a (d - d_c) expansion. We also argue that there
is a intriguing possibility that the rough phases above and below the lower
critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead
to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett.
style files included; slightly expanded reincarnatio
Resonance structures in the multichannel quantum defect theory for the photofragmentation processes involving one closed and many open channels
The transformation introduced by Giusti-Suzor and Fano and extended by
Lecomte and Ueda for the study of resonance structures in the multichannel
quantum defect theory (MQDT) is used to reformulate MQDT into the forms having
one-to-one correspondence with those in Fano's configuration mixing (CM) theory
of resonance for the photofragmentation processes involving one closed and many
open channels. The reformulation thus allows MQDT to have the full power of the
CM theory, still keeping its own strengths such as the fundamental description
of resonance phenomena without an assumption of the presence of a discrete
state as in CM.Comment: 7 page
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