1,578 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
A Semiparametric Test of Agent's Information Sets for Games of Incomplete Information
We propose semiparametric tests of misspecification of agent's information for games of incomplete information. The tests use the intuition that the opponent's choices should not predict a player's choice conditional on the proposed information available to the player. The tests are designed to check against some commonly used null hypotheses (Bajari et al. (2010), Aradillas-Lopez (2010)). We show that our tests have power to discriminate between common alternatives even in small samples. We apply our tests to data on entry in the US airline industry. Both the assumptions of independent and correlated private shocks are not supported by the data
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
Semiparametric GEE analysis in partially linear single-index models for longitudinal data
In this article, we study a partially linear single-index model for
longitudinal data under a general framework which includes both the sparse and
dense longitudinal data cases. A semiparametric estimation method based on a
combination of the local linear smoothing and generalized estimation equations
(GEE) is introduced to estimate the two parameter vectors as well as the
unknown link function. Under some mild conditions, we derive the asymptotic
properties of the proposed parametric and nonparametric estimators in different
scenarios, from which we find that the convergence rates and asymptotic
variances of the proposed estimators for sparse longitudinal data would be
substantially different from those for dense longitudinal data. We also discuss
the estimation of the covariance (or weight) matrices involved in the
semiparametric GEE method. Furthermore, we provide some numerical studies
including Monte Carlo simulation and an empirical application to illustrate our
methodology and theory.Comment: Published at http://dx.doi.org/10.1214/15-AOS1320 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Inverse Optimization with Noisy Data
Inverse optimization refers to the inference of unknown parameters of an
optimization problem based on knowledge of its optimal solutions. This paper
considers inverse optimization in the setting where measurements of the optimal
solutions of a convex optimization problem are corrupted by noise. We first
provide a formulation for inverse optimization and prove it to be NP-hard. In
contrast to existing methods, we show that the parameter estimates produced by
our formulation are statistically consistent. Our approach involves combining a
new duality-based reformulation for bilevel programs with a regularization
scheme that smooths discontinuities in the formulation. Using epi-convergence
theory, we show the regularization parameter can be adjusted to approximate the
original inverse optimization problem to arbitrary accuracy, which we use to
prove our consistency results. Next, we propose two solution algorithms based
on our duality-based formulation. The first is an enumeration algorithm that is
applicable to settings where the dimensionality of the parameter space is
modest, and the second is a semiparametric approach that combines nonparametric
statistics with a modified version of our formulation. These numerical
algorithms are shown to maintain the statistical consistency of the underlying
formulation. Lastly, using both synthetic and real data, we demonstrate that
our approach performs competitively when compared with existing heuristics
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
Automated Discovery in Econometrics
Our subject is the notion of automated discovery in econometrics. Advances in computer power, electronic communication, and data collection processes have all changed the way econometrics is conducted. These advances have helped to elevate the status of empirical research within the economics profession in recent years and they now open up new possibilities for empirical econometric practice. Of particular significance is the ability to build econometric models in an automated way according to an algorithm of decision rules that allow for (what we call here) heteroskedastic and autocorrelation robust (HAR) inference. Computerized search algorithms may be implemented to seek out suitable models, thousands of regressions and model evaluations may be performed in seconds, statistical inference may be automated according to the properties of the data, and policy decisions can be made and adjusted in real time with the arrival of new data. We discuss some aspects and implications of these exciting, emergent trends in econometrics.Automation, discovery, HAC estimation, HAR inference, model building, online econometrics, policy analysis, prediction, trends
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