2,954 research outputs found
Uniform asymptotics for robust location estimates when the scale is unknown
Most asymptotic results for robust estimates rely on regularity conditions
that are difficult to verify in practice. Moreover, these results apply to
fixed distribution functions. In the robustness context the distribution of the
data remains largely unspecified and hence results that hold uniformly over a
set of possible distribution functions are of theoretical and practical
interest. Also, it is desirable to be able to determine the size of the set of
distribution functions where the uniform properties hold. In this paper we
study the problem of obtaining verifiable regularity conditions that suffice to
yield uniform consistency and uniform asymptotic normality for location robust
estimates when the scale of the errors is unknown.
We study M-location estimates calculated with an S-scale and we obtain
uniform asymptotic results over contamination neighborhoods. Moreover, we show
how to calculate the maximum size of the contamination neighborhoods where
these uniform results hold. There is a trade-off between the size of these
neighborhoods and the breakdown point of the scale estimate.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Statistics
(http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000054
Uniform asymptotics for robust location estimates when the scale is unknown
Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verify and that real data sets rarely satisfy. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data remains largely unspecified and hence results that hold uniformly over a set of possible distribution functions are of theoretical and practical interest. In this paper we study the problem of obtaining verifiable and realistic conditions that suffice to obtain uniform consistency and uniform asymptotic normality for location robust estimates when the scale of the errors is unknown. We study M-location estimates calculated withan S-scale and we obtain uniform asymptotic results over contamination neighbourhoods. There is a trade-off between the size of these neighbourhoods and the breakdown point of the scale estimate. We also show how to calculate the maximum size of the contamination neighbourhoods where these uniform results hold.
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
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
CMB Polarization Experiments
We discuss the analysis of polarization experiments with particular emphasis
on those that measure the Stokes parameters on a ring on the sky. We discuss
the ability of these experiments to separate the and contributions to
the polarization signal. The experiment being developed at Wisconsin university
is studied in detail, it will be sensitive to both Stokes parameters and will
concentrate on large scale polarization, scanning a degree ring. We will
also consider another example, an experiment that measures one of the Stokes
parameters in a ring. We find that the small ring experiment will be able
to detect cosmological polarization for some models consistent with the current
temperature anisotropy data, for reasonable integration times. In most
cosmological models large scale polarization is too small to be detected by the
Wisconsin experiment, but because both and are measured, separate
constraints can be set on and polarization.Comment: 27 pages with 12 included figure
Binscatter Regressions
We introduce the \texttt{Stata} (and \texttt{R}) package \textsf{Binsreg},
which implements the binscatter methods developed in
\citet*{Cattaneo-Crump-Farrell-Feng_2019_Binscatter}. The package includes the
commands \texttt{binsreg}, \texttt{binsregtest}, and \texttt{binsregselect}.
The first command (\texttt{binsreg}) implements binscatter for the regression
function and its derivatives, offering several point estimation, confidence
intervals and confidence bands procedures, with particular focus on
constructing binned scatter plots. The second command (\texttt{binsregtest})
implements hypothesis testing procedures for parametric specification and for
nonparametric shape restrictions of the unknown regression function. Finally,
the third command (\texttt{binsregselect}) implements data-driven number of
bins selectors for binscatter implementation using either quantile-spaced or
evenly-spaced binning/partitioning. All the commands allow for covariate
adjustment, smoothness restrictions, weighting and clustering, among other
features. A companion \texttt{R} package with the same capabilities is also
available
Combining Full-Shape and BAO Analyses of Galaxy Power Spectra: A 1.6% CMB-independent constraint on H0
We present cosmological constraints from a joint analysis of the pre- and
post-reconstruction galaxy power spectrum multipoles from the final data
release of the Baryon Oscillation Spectroscopic Survey (BOSS). Geometric
constraints are obtained from the positions of BAO peaks in reconstructed
spectra, analyzed in combination with the unreconstructed spectra in a
full-shape (FS) likelihood using a joint covariance matrix, giving stronger
parameter constraints than FS-only or BAO-only analyses. We introduce a new
method for obtaining constraints from reconstructed spectra based on a
correlated theoretical error, which is shown to be simple, robust, and
applicable to any flavor of density-field reconstruction. Assuming CDM
with massive neutrinos, we analyze data from two redshift bins
and obtain constraints on the Hubble
constant , using only a single prior on the current baryon density
from Big Bang Nucleosynthesis (BBN) and no knowledge of the power
spectrum slope . This gives , with the inclusion of BAO
data sharpening the measurement by , representing one of the strongest
current constraints on independent of cosmic microwave background data.
Restricting to the best-fit slope from Planck (but without additional
priors on the spectral shape), we obtain a measurement of . We find strong constraints on the
cosmological parameters from a joint analysis of the FS, BAO, and Planck data.
This sets new bounds on the sum of neutrino masses (at confidence) and the effective number of
relativistic degrees of freedom , though
contours are not appreciably narrowed by the inclusion of BAO data.Comment: 42 pages, 12 figures, accepted by JCAP, likelihoods available at
https://github.com/Michalychforever/lss_montepython (minor typo corrected
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