2,879 research outputs found
Backfitting and smooth backfitting for additive quantile models
In this paper, we study the ordinary backfitting and smooth backfitting as
methods of fitting additive quantile models. We show that these backfitting
quantile estimators are asymptotically equivalent to the corresponding
backfitting estimators of the additive components in a specially-designed
additive mean regression model. This implies that the theoretical properties of
the backfitting quantile estimators are not unlike those of backfitting mean
regression estimators. We also assess the finite sample properties of the two
backfitting quantile estimators.Comment: Published in at http://dx.doi.org/10.1214/10-AOS808 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org). With Correction
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
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