42,134 research outputs found
Single-index quantile regression
This is the post-print version of the final paper published in Journal of Multivariate Analysis. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.Nonparametric quantile regression with multivariate covariates is a difficult estimation problem due to the “curse of dimensionality”. To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a single-index function View the MathML sourceg0(xTγ0), where a univariate link function g0(⋅)g0(⋅) is applied to a linear combination of covariates View the MathML sourcexTγ0, often called the single-index. We introduce a practical algorithm where the unknown link function g0(⋅)g0(⋅) is estimated by local linear quantile regression and the parametric index is estimated through linear quantile regression. Large sample properties of estimators are studied, which facilitate further inference. Both the modeling and estimation approaches are demonstrated by simulation studies and real data applications
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
Bayesian Quantile Regression for Single-Index Models
Using an asymmetric Laplace distribution, which provides a mechanism for
Bayesian inference of quantile regression models, we develop a fully Bayesian
approach to fitting single-index models in conditional quantile regression. In
this work, we use a Gaussian process prior for the unknown nonparametric link
function and a Laplace distribution on the index vector, with the latter
motivated by the recent popularity of the Bayesian lasso idea. We design a
Markov chain Monte Carlo algorithm for posterior inference. Careful
consideration of the singularity of the kernel matrix, and tractability of some
of the full conditional distributions leads to a partially collapsed approach
where the nonparametric link function is integrated out in some of the sampling
steps. Our simulations demonstrate the superior performance of the Bayesian
method versus the frequentist approach. The method is further illustrated by an
application to the hurricane data.Comment: 26 pages, 8 figures, 10 table
Quantile Estimation of A general Single-Index Model
The single-index model is one of the most popular semiparametric models in
Econometrics. In this paper, we define a quantile regression single-index
model, which includes the single-index structure for conditional mean and for
conditional variance.Comment: 32page
Estimating Generalized Additive Conditional Quantiles for Absolutely Regular Processes
We propose a nonparametric method for estimating the conditional quantile
function that admits a generalized additive specification with an unknown link
function. This model nests single-index, additive, and multiplicative quantile
regression models. Based on a full local linear polynomial expansion, we first
obtain the asymptotic representation for the proposed quantile estimator for
each additive component. Then, the link function is estimated by noting that it
corresponds to the conditional quantile function of a response variable given
the sum of all additive components. The observations are supposed to be a
sample from a strictly stationary and absolutely regular process. We provide
results on (uniform) consistency rates, second order asymptotic expansions and
point wise asymptotic normality of each proposed estimator
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