14,182 research outputs found
Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates
We study semiparametric varying-coefficient partially linear models when some
linear covariates are not observed, but ancillary variables are available.
Semiparametric profile least-square based estimation procedures are developed
for parametric and nonparametric components after we calibrate the error-prone
covariates. Asymptotic properties of the proposed estimators are established.
We also propose the profile least-square based ratio test and Wald test to
identify significant parametric and nonparametric components. To improve
accuracy of the proposed tests for small or moderate sample sizes, a wild
bootstrap version is also proposed to calculate the critical values. Intensive
simulation experiments are conducted to illustrate the proposed approaches.Comment: Published in at http://dx.doi.org/10.1214/07-AOS561 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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
Focused information criterion and model averaging for generalized additive partial linear models
We study model selection and model averaging in generalized additive partial
linear models (GAPLMs). Polynomial spline is used to approximate nonparametric
functions. The corresponding estimators of the linear parameters are shown to
be asymptotically normal. We then develop a focused information criterion (FIC)
and a frequentist model average (FMA) estimator on the basis of the
quasi-likelihood principle and examine theoretical properties of the FIC and
FMA. The major advantages of the proposed procedures over the existing ones are
their computational expediency and theoretical reliability. Simulation
experiments have provided evidence of the superiority of the proposed
procedures. The approach is further applied to a real-world data example.Comment: Published in at http://dx.doi.org/10.1214/10-AOS832 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model
Modeling viral dynamics in HIV/AIDS studies has resulted in a deep
understanding of pathogenesis of HIV infection from which novel antiviral
treatment guidance and strategies have been derived. Viral dynamics models
based on nonlinear differential equations have been proposed and well developed
over the past few decades. However, it is quite challenging to use experimental
or clinical data to estimate the unknown parameters (both constant and
time-varying parameters) in complex nonlinear differential equation models.
Therefore, investigators usually fix some parameter values, from the literature
or by experience, to obtain only parameter estimates of interest from clinical
or experimental data. However, when such prior information is not available, it
is desirable to determine all the parameter estimates from data. In this paper
we intend to combine the newly developed approaches, a multi-stage
smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares
(SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear
differential equation model. In particular, to the best of our knowledge, this
is the first attempt to propose a comparatively thorough procedure, accounting
for both efficiency and accuracy, to rigorously estimate all key kinetic
parameters in a nonlinear differential equation model of HIV dynamics from
clinical data. These parameters include the proliferation rate and death rate
of uninfected HIV-targeted cells, the average number of virions produced by an
infected cell, and the infection rate which is related to the antiviral
treatment effect and is time-varying. To validate the estimation methods, we
verified the identifiability of the HIV viral dynamic model and performed
simulation studies.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS290 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Penalized variable selection procedure for Cox models with semiparametric relative risk
We study the Cox models with semiparametric relative risk, which can be
partially linear with one nonparametric component, or multiple additive or
nonadditive nonparametric components. A penalized partial likelihood procedure
is proposed to simultaneously estimate the parameters and select variables for
both the parametric and the nonparametric parts. Two penalties are applied
sequentially. The first penalty, governing the smoothness of the multivariate
nonlinear covariate effect function, provides a smoothing spline ANOVA
framework that is exploited to derive an empirical model selection tool for the
nonparametric part. The second penalty, either the
smoothly-clipped-absolute-deviation (SCAD) penalty or the adaptive LASSO
penalty, achieves variable selection in the parametric part. We show that the
resulting estimator of the parametric part possesses the oracle property, and
that the estimator of the nonparametric part achieves the optimal rate of
convergence. The proposed procedures are shown to work well in simulation
experiments, and then applied to a real data example on sexually transmitted
diseases.Comment: Published in at http://dx.doi.org/10.1214/09-AOS780 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
- …