7,077 research outputs found
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
Estimation of treatment effects with high-dimensional controls
We propose methods for inference on the average effect of a treatment on a scalar outcome in the presence of very many controls. Our setting is a partially linear regression model containing the treatment/policy variable and a large number p of controls or series terms, with p that is possibly much larger than the sample size n, but where only s << n unknown controls or series terms are needed to approximate the regression function accurately. The latter sparsity condition makes it possible to estimate the entire regression function as well as the average treatment effect by selecting an approximately the right set of controls using Lasso and related methods. We develop estimation and inference methods for the average treatment effect in this setting, proposing a novel "post double selection" method that provides attractive inferential and estimation properties. In our analysis, in order to cover realistic applications, we expressly allow for imperfect selection of the controls and account for the impact of selection errors on estimation and inference. In order to cover typical applications in economics, we employ the selection methods designed to deal with non-Gaussian and heteroscedastic disturbances. We illustrate the use of new methods with numerical simulations and an application to the effect of abortion on crime rates.
Modeling of optical amplifier waveguide based on silicon nanostructures and rare earth ions doped silica matrix gain media by a finite-difference time-domain method: comparison of achievable gain with Er3+ or Nd3+ ions dopants
A comparative study of the gain achievement is performed in a waveguide
optical amplifier whose active layer is constituted by a silica matrix
containing silicon nanograins acting as sensitizer of either neodymium ions (Nd
3+) or erbium ions (Er 3+). Due to the large difference between population
levels characteristic times (ms) and finite-difference time step (10 --17 s),
the conventional auxiliary differential equation and finite-difference
time-domain (ADE-FDTD) method is not appropriate to treat such systems.
Consequently, a new two loops algorithm based on ADE-FDTD method is presented
in order to model this waveguide optical amplifier. We investigate the steady
states regime of both rare earth ions and silicon nanograins levels populations
as well as the electromagnetic field for different pumping powers ranging from
1 to 10 4 mW.mm-2. Furthermore, the three dimensional distribution of
achievable gain per unit length has been estimated in this pumping range. The
Nd 3+ doped waveguide shows a higher gross gain per unit length at 1064 nm (up
to 30 dB.cm-1) than the one with Er 3+ doped active layer at 1532 nm (up to 2
dB.cm-1). Considering the experimental background losses found on those
waveguides we demonstrate that a significant positive net gain can only be
achieved with the Nd 3+ doped waveguide. The developed algorithm is stable and
applicable to optical gain materials with emitters having a wide range of
characteristic lifetimes.Comment: Photonics West , Feb 2015, San Francisco, United States. S, SPIE
Proceedings, 9357 (935709), 2015, Physics and Simulation of Optoelectronic
Devices XXIII. arXiv admin note: text overlap with arXiv:1405.533
Theoretical investigation of the more suitable rare earth to achieve high gain in waveguide based on silica containing silicon nanograins doped with either Nd3+ or Er3+ ions
We present a comparative study of the gain achievement in a waveguide whose
active layer is constituted by a silica matrix containing silicon nanograins
acting as sensitizer of either neodymium ions (Nd3+) or erbium ions (Er3+). By
means of an auxiliary differential equation and finite difference time domain
(ADE-FDTD) approach that we developed, we investigate the steady states regime
of both rare earths ions and silicon nanograins levels populations as well as
the electromagnetic field for different pumping powers ranging from 1 to 104
mW/mm2. Moreover, the achievable gain has been estimated in this pumping range.
The Nd3+ doped waveguide shows a higher gross gain per unit length at 1064 nm
(up to 30 dB/cm) than the one with Er3+ doped active layer at 1532 nm (up to 2
dB/cm). Taking into account the experimental background losses we demonstrate
that a significant positive net gain can only be achieved with the Nd3+ doped
waveguide
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