21,292 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
Robust nonparametric estimation via wavelet median regression
In this paper we develop a nonparametric regression method that is
simultaneously adaptive over a wide range of function classes for the
regression function and robust over a large collection of error distributions,
including those that are heavy-tailed, and may not even possess variances or
means. Our approach is to first use local medians to turn the problem of
nonparametric regression with unknown noise distribution into a standard
Gaussian regression problem and then apply a wavelet block thresholding
procedure to construct an estimator of the regression function. It is shown
that the estimator simultaneously attains the optimal rate of convergence over
a wide range of the Besov classes, without prior knowledge of the smoothness of
the underlying functions or prior knowledge of the error distribution. The
estimator also automatically adapts to the local smoothness of the underlying
function, and attains the local adaptive minimax rate for estimating functions
at a point. A key technical result in our development is a quantile coupling
theorem which gives a tight bound for the quantile coupling between the sample
medians and a normal variable. This median coupling inequality may be of
independent interest.Comment: Published in at http://dx.doi.org/10.1214/07-AOS513 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Choosing the Right Spatial Weighting Matrix in a Quantile Regression Model
This paper proposes computationally tractable methods for selecting the appropriate spatial weighting matrix in the context of a spatial quantile regression model. This selection is a notoriously difficult problem even in linear spatial models and is even more difficult in a quantile regression setup. The proposal is illustrated by an empirical example and manages to produce tractable models. One important feature of the proposed methodology is that by allowing different degrees and forms of spatial dependence across quantiles it further relaxes the usual quantile restriction attributable to the linear quantile regression. In this way we can obtain a more robust, with regard to potential functional misspecification, model, but nevertheless preserve the parametric rate of convergence and the established inferential apparatus associated with the linear quantile regression approach
Binscatter Regressions
We introduce the \texttt{Stata} (and \texttt{R}) package \textsf{Binsreg},
which implements the binscatter methods developed in
\citet*{Cattaneo-Crump-Farrell-Feng_2019_Binscatter}. The package includes the
commands \texttt{binsreg}, \texttt{binsregtest}, and \texttt{binsregselect}.
The first command (\texttt{binsreg}) implements binscatter for the regression
function and its derivatives, offering several point estimation, confidence
intervals and confidence bands procedures, with particular focus on
constructing binned scatter plots. The second command (\texttt{binsregtest})
implements hypothesis testing procedures for parametric specification and for
nonparametric shape restrictions of the unknown regression function. Finally,
the third command (\texttt{binsregselect}) implements data-driven number of
bins selectors for binscatter implementation using either quantile-spaced or
evenly-spaced binning/partitioning. All the commands allow for covariate
adjustment, smoothness restrictions, weighting and clustering, among other
features. A companion \texttt{R} package with the same capabilities is also
available
Inference for High-Dimensional Sparse Econometric Models
This article is about estimation and inference methods for high dimensional
sparse (HDS) regression models in econometrics. High dimensional sparse models
arise in situations where many regressors (or series terms) are available and
the regression function is well-approximated by a parsimonious, yet unknown set
of regressors. The latter condition makes it possible to estimate the entire
regression function effectively by searching for approximately the right set of
regressors. We discuss methods for identifying this set of regressors and
estimating their coefficients based on -penalization and describe key
theoretical results. In order to capture realistic practical situations, we
expressly allow for imperfect selection of regressors and study the impact of
this imperfect selection on estimation and inference results. We focus the main
part of the article on the use of HDS models and methods in the instrumental
variables model and the partially linear model. We present a set of novel
inference results for these models and illustrate their use with applications
to returns to schooling and growth regression
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