19,782 research outputs found
Variable selection in semiparametric regression modeling
In this paper, we are concerned with how to select significant variables in
semiparametric modeling. Variable selection for semiparametric regression
models consists of two components: model selection for nonparametric components
and selection of significant variables for the parametric portion. Thus,
semiparametric variable selection is much more challenging than parametric
variable selection (e.g., linear and generalized linear models) because
traditional variable selection procedures including stepwise regression and the
best subset selection now require separate model selection for the
nonparametric components for each submodel. This leads to a very heavy
computational burden. In this paper, we propose a class of variable selection
procedures for semiparametric regression models using nonconcave penalized
likelihood. We establish the rate of convergence of the resulting estimate.
With proper choices of penalty functions and regularization parameters, we show
the asymptotic normality of the resulting estimate and further demonstrate that
the proposed procedures perform as well as an oracle procedure. A
semiparametric generalized likelihood ratio test is proposed to select
significant variables in the nonparametric component. We investigate the
asymptotic behavior of the proposed test and demonstrate that its limiting null
distribution follows a chi-square distribution which is independent of the
nuisance parameters. Extensive Monte Carlo simulation studies are conducted to
examine the finite sample performance of the proposed variable selection
procedures.Comment: Published in at http://dx.doi.org/10.1214/009053607000000604 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bias in parametric estimation: reduction and useful side-effects
The bias of an estimator is defined as the difference of its expected value
from the parameter to be estimated, where the expectation is with respect to
the model. Loosely speaking, small bias reflects the desire that if an
experiment is repeated indefinitely then the average of all the resultant
estimates will be close to the parameter value that is estimated. The current
paper is a review of the still-expanding repository of methods that have been
developed to reduce bias in the estimation of parametric models. The review
provides a unifying framework where all those methods are seen as attempts to
approximate the solution of a simple estimating equation. Of particular focus
is the maximum likelihood estimator, which despite being asymptotically
unbiased under the usual regularity conditions, has finite-sample bias that can
result in significant loss of performance of standard inferential procedures.
An informal comparison of the methods is made revealing some useful practical
side-effects in the estimation of popular models in practice including: i)
shrinkage of the estimators in binomial and multinomial regression models that
guarantees finiteness even in cases of data separation where the maximum
likelihood estimator is infinite, and ii) inferential benefits for models that
require the estimation of dispersion or precision parameters
Functional Structure and Approximation in Econometrics (book front matter)
This is the front matter from the book, William A. Barnett and Jane Binner (eds.), Functional Structure and Approximation in Econometrics, published in 2004 by Elsevier in its Contributions to Economic Analysis monograph series. The front matter includes the Table of Contents, Volume Introduction, and Section Introductions by Barnett and Binner and the Preface by W. Erwin Diewert. The volume contains a unified collection and discussion of W. A. Barnett's most important published papers on applied and theoretical econometric modelling.consumer demand, production, flexible functional form, functional structure, asymptotics, nonlinearity, systemwide models
Point estimation with exponentially tilted empirical likelihood
Parameters defined via general estimating equations (GEE) can be estimated by
maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72
(2004) 219--255] have recently shown that this EL estimator exhibits desirable
higher-order asymptotic properties, namely, that its bias is small
and that bias-corrected EL is higher-order efficient. Although EL possesses
these properties when the model is correctly specified, this paper shows that,
in the presence of model misspecification, EL may cease to be root n convergent
when the functions defining the moment conditions are unbounded (even when
their expectations are bounded). In contrast, the related exponential tilting
(ET) estimator avoids this problem. This paper shows that the ET and EL
estimators can be naturally combined to yield an estimator called exponentially
tilted empirical likelihood (ETEL) exhibiting the same bias and the
same variance as EL, while maintaining root n convergence under
model misspecification.Comment: Published at http://dx.doi.org/10.1214/009053606000001208 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- âŠ