8,123 research outputs found
Estimating spatial quantile regression with functional coefficients: A robust semiparametric framework
This paper considers an estimation of semiparametric functional
(varying)-coefficient quantile regression with spatial data. A general robust
framework is developed that treats quantile regression for spatial data in a
natural semiparametric way. The local M-estimators of the unknown
functional-coefficient functions are proposed by using local linear
approximation, and their asymptotic distributions are then established under
weak spatial mixing conditions allowing the data processes to be either
stationary or nonstationary with spatial trends. Application to a soil data set
is demonstrated with interesting findings that go beyond traditional analysis.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ480 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Quantile regression in partially linear varying coefficient models
Semiparametric models are often considered for analyzing longitudinal data
for a good balance between flexibility and parsimony. In this paper, we study a
class of marginal partially linear quantile models with possibly varying
coefficients. The functional coefficients are estimated by basis function
approximations. The estimation procedure is easy to implement, and it requires
no specification of the error distributions. The asymptotic properties of the
proposed estimators are established for the varying coefficients as well as for
the constant coefficients. We develop rank score tests for hypotheses on the
coefficients, including the hypotheses on the constancy of a subset of the
varying coefficients. Hypothesis testing of this type is theoretically
challenging, as the dimensions of the parameter spaces under both the null and
the alternative hypotheses are growing with the sample size. We assess the
finite sample performance of the proposed method by Monte Carlo simulation
studies, and demonstrate its value by the analysis of an AIDS data set, where
the modeling of quantiles provides more comprehensive information than the
usual least squares approach.Comment: Published in at http://dx.doi.org/10.1214/09-AOS695 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Quantile regression with varying coefficients
Quantile regression provides a framework for modeling statistical quantities
of interest other than the conditional mean. The regression methodology is well
developed for linear models, but less so for nonparametric models. We consider
conditional quantiles with varying coefficients and propose a methodology for
their estimation and assessment using polynomial splines. The proposed
estimators are easy to compute via standard quantile regression algorithms and
a stepwise knot selection algorithm. The proposed Rao-score-type test that
assesses the model against a linear model is also easy to implement. We provide
asymptotic results on the convergence of the estimators and the null
distribution of the test statistic. Empirical results are also provided,
including an application of the methodology to forced expiratory volume (FEV)
data.Comment: Published at http://dx.doi.org/10.1214/009053606000000966 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Discussion paper. Conditional growth charts
Growth charts are often more informative when they are customized per
subject, taking into account prior measurements and possibly other covariates
of the subject. We study a global semiparametric quantile regression model that
has the ability to estimate conditional quantiles without the usual
distributional assumptions. The model can be estimated from longitudinal
reference data with irregular measurement times and with some level of
robustness against outliers, and it is also flexible for including covariate
information. We propose a rank score test for large sample inference on
covariates, and develop a new model assessment tool for longitudinal growth
data. Our research indicates that the global model has the potential to be a
very useful tool in conditional growth chart analysis.Comment: This paper discussed in: [math/0702636], [math/0702640],
[math/0702641], [math/0702642]. Rejoinder in [math.ST/0702643]. Published at
http://dx.doi.org/10.1214/009053606000000623 in the Annals of Statistics
(http://www.imstat.org/aos/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Conditional Transformation Models
The ultimate goal of regression analysis is to obtain information about the
conditional distribution of a response given a set of explanatory variables.
This goal is, however, seldom achieved because most established regression
models only estimate the conditional mean as a function of the explanatory
variables and assume that higher moments are not affected by the regressors.
The underlying reason for such a restriction is the assumption of additivity of
signal and noise. We propose to relax this common assumption in the framework
of transformation models. The novel class of semiparametric regression models
proposed herein allows transformation functions to depend on explanatory
variables. These transformation functions are estimated by regularised
optimisation of scoring rules for probabilistic forecasts, e.g. the continuous
ranked probability score. The corresponding estimated conditional distribution
functions are consistent. Conditional transformation models are potentially
useful for describing possible heteroscedasticity, comparing spatially varying
distributions, identifying extreme events, deriving prediction intervals and
selecting variables beyond mean regression effects. An empirical investigation
based on a heteroscedastic varying coefficient simulation model demonstrates
that semiparametric estimation of conditional distribution functions can be
more beneficial than kernel-based non-parametric approaches or parametric
generalised additive models for location, scale and shape
Penalized single-index quantile regression
This article is made available through the Brunel Open Access Publishing Fund. Copyright for this article is retained by the author(s), with first publication rights granted to the journal.
This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution
license (http://creativecommons.org/licenses/by/3.0/).The single-index (SI) regression and single-index quantile (SIQ) estimation methods product linear combinations of all the original predictors. However, it is possible that there are many unimportant predictors within the original predictors. Thus, the precision of parameter estimation as well as the accuracy of prediction will be effected by the existence of those unimportant predictors when the previous methods are used. In this article, an extension of the SIQ method of Wu et al. (2010) has been proposed, which considers Lasso and Adaptive Lasso for estimation and variable selection. Computational algorithms have been developed in order to calculate the penalized SIQ estimates. A simulation study and a real data application have been used to assess the performance of the methods under consideration
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