361 research outputs found
Optimal Bandwidth Choice for Robust Bias Corrected Inference in Regression Discontinuity Designs
Modern empirical work in Regression Discontinuity (RD) designs often employs
local polynomial estimation and inference with a mean square error (MSE)
optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment
effect estimator, but is by construction invalid for inference. Robust bias
corrected (RBC) inference methods are valid when using the MSE-optimal
bandwidth, but we show they yield suboptimal confidence intervals in terms of
coverage error. We establish valid coverage error expansions for RBC confidence
interval estimators and use these results to propose new inference-optimal
bandwidth choices for forming these intervals. We find that the standard
MSE-optimal bandwidth for the RD point estimator is too large when the goal is
to construct RBC confidence intervals with the smallest coverage error. We
further optimize the constant terms behind the coverage error to derive new
optimal choices for the auxiliary bandwidth required for RBC inference. Our
expansions also establish that RBC inference yields higher-order refinements
(relative to traditional undersmoothing) in the context of RD designs. Our main
results cover sharp and sharp kink RD designs under conditional
heteroskedasticity, and we discuss extensions to fuzzy and other RD designs,
clustered sampling, and pre-intervention covariates adjustments. The
theoretical findings are illustrated with a Monte Carlo experiment and an
empirical application, and the main methodological results are available in
\texttt{R} and \texttt{Stata} packages
Bayesian inference of a negative quantity from positive measurement results
In this paper the Bayesian analysis is applied to assign a probability
density to the value of a quantity having a definite sign. This analysis is
logically consistent with the results, positive or negative, of repeated
measurements. Results are used to estimate the atom density shift in a caesium
fountain clock. The comparison with the classical statistical analysis is also
reported and the advantages of the Bayesian approach for the realization of the
time unit are discussed.Comment: 10 pages, 4 figures, submitted to Metrologi
On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference
Nonparametric methods play a central role in modern empirical work. While
they provide inference procedures that are more robust to parametric
misspecification bias, they may be quite sensitive to tuning parameter choices.
We study the effects of bias correction on confidence interval coverage in the
context of kernel density and local polynomial regression estimation, and prove
that bias correction can be preferred to undersmoothing for minimizing coverage
error and increasing robustness to tuning parameter choice. This is achieved
using a novel, yet simple, Studentization, which leads to a new way of
constructing kernel-based bias-corrected confidence intervals. In addition, for
practical cases, we derive coverage error optimal bandwidths and discuss
easy-to-implement bandwidth selectors. For interior points, we show that the
MSE-optimal bandwidth for the original point estimator (before bias correction)
delivers the fastest coverage error decay rate after bias correction when
second-order (equivalent) kernels are employed, but is otherwise suboptimal
because it is too "large". Finally, for odd-degree local polynomial regression,
we show that, as with point estimation, coverage error adapts to boundary
points automatically when appropriate Studentization is used; however, the
MSE-optimal bandwidth for the original point estimator is suboptimal. All the
results are established using valid Edgeworth expansions and illustrated with
simulated data. Our findings have important consequences for empirical work as
they indicate that bias-corrected confidence intervals, coupled with
appropriate standard errors, have smaller coverage error and are less sensitive
to tuning parameter choices in practically relevant cases where additional
smoothness is available
Regression Discontinuity Designs Using Covariates
We study regression discontinuity designs when covariates are included in the
estimation. We examine local polynomial estimators that include discrete or
continuous covariates in an additive separable way, but without imposing any
parametric restrictions on the underlying population regression functions. We
recommend a covariate-adjustment approach that retains consistency under
intuitive conditions, and characterize the potential for estimation and
inference improvements. We also present new covariate-adjusted mean squared
error expansions and robust bias-corrected inference procedures, with
heteroskedasticity-consistent and cluster-robust standard errors. An empirical
illustration and an extensive simulation study is presented. All methods are
implemented in \texttt{R} and \texttt{Stata} software packages
Realization of a twin beam source based on four-wave mixing in Cesium
Four-wave mixing (4WM) is a known source of intense non-classical twin beams.
It can be generated when an intense laser beam (the pump) and a weak laser beam
(the seed) overlap in a medium (here cesium vapor), with
frequencies close to resonance with atomic transitions. The twin beams
generated by 4WM have frequencies naturally close to atomic transitions, and
can be intense (gain ) even in the CW pump regime, which is not the case
for PDC phenomenon in non-linear crystals. So, 4WM is well suited
for atom-light interaction and atom-based quantum protocols. Here we present
the first realization of a source of 4-wave mixing exploiting line of
Cesium atoms.Comment: 10 pages, 10 figure
Generation of an ultrastable 578 nm laser for Yb lattice clock
In this paper we described the development and the characterization of a 578 nm laser source to be the clock laser for an Ytterbium Lattice Optical clock. Two independent laser sources have been realized and the characterization of the stability with a beat note technique is presente
nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference
Nonparametric kernel density and local polynomial regression estimators are very popular in statistics, economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as a preliminary ingredient entering some other estimation or inference procedure. This article describes the main methodological and numerical features of the software package nprobust, which offers an array of estimation and inference procedures for nonparametric kernel-based density and local polynomial regression methods, implemented in both the R and Stata statistical platforms. The package includes not only classical bandwidth selection, estimation, and inference methods (Wand and Jones 1995; Fan and Gijbels 1996), but also other recent developments in the statistics and econometrics literatures such as robust bias-corrected inference and coverage error optimal bandwidth selection (Calonico, Cattaneo, and Farrell 2018, 2019a). Furthermore, this article also proposes a simple way of estimating optimal bandwidths in practice that always delivers the optimal mean square error convergence rate regardless of the specific evaluation point, that is, no matter whether it is implemented at a boundary or interior point. Numerical performance is illustrated using an empirical application and simulated data, where a detailed numerical comparison with other R packages is given
nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference
Nonparametric kernel density and local polynomial regression estimators are
very popular in Statistics, Economics, and many other disciplines. They are
routinely employed in applied work, either as part of the main empirical
analysis or as a preliminary ingredient entering some other estimation or
inference procedure. This article describes the main methodological and
numerical features of the software package nprobust, which offers an array of
estimation and inference procedures for nonparametric kernel-based density and
local polynomial regression methods, implemented in both the R and Stata
statistical platforms. The package includes not only classical bandwidth
selection, estimation, and inference methods (Wand and Jones, 1995; Fan and
Gijbels, 1996), but also other recent developments in the statistics and
econometrics literatures such as robust bias-corrected inference and coverage
error optimal bandwidth selection (Calonico, Cattaneo and Farrell, 2018, 2019).
Furthermore, this article also proposes a simple way of estimating optimal
bandwidths in practice that always delivers the optimal mean square error
convergence rate regardless of the specific evaluation point, that is, no
matter whether it is implemented at a boundary or interior point. Numerical
performance is illustrated using an empirical application and simulated data,
where a detailed numerical comparison with other R packages is given
Measurement of the Blackbody Radiation Shift of the 133Cs Hyperfine Transition in an Atomic Fountain
We used a Cs atomic fountain frequency standard to measure the Stark shift on
the ground state hyperfine transiton frequency in cesium (9.2 GHz) due to the
electric field generated by the blackbody radiation. The measures relative
shift at 300 K is -1.43(11)e-14 and agrees with our theoretical evaluation
-1.49(07)e-14. This value differs from the currently accepted one
-1.69(04)e-14. The difference has a significant implication on the accuracy of
frequency standards, in clocks comparison, and in a variety of high precision
physics tests such as the time stability of fundamental constants.Comment: 4 pages, 2 figures, 2 table
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