3,797 research outputs found
The Shift of the Baryon Acoustic Oscillation Scale: A Simple Physical Picture
A shift of the baryon acoustic oscillation (BAO) scale to smaller values than
predicted by linear theory was observed in simulations. In this paper, we try
to provide an intuitive physical understanding of why this shift occurs,
explaining in more pedagogical detail earlier perturbation theory calculations.
We find that the shift is mainly due to the following physical effect. A
measurement of the BAO scale is more sensitive to regions with long wavelength
overdensities than underdensities, because (due to non-linear growth and bias)
these overdense regions contain larger fluctuations and more tracers and hence
contribute more to the total correlation function. In overdense regions the BAO
scale shrinks because such regions locally behave as positively curved closed
universes, and hence a smaller scale than predicted by linear theory is
measured in the total correlation function. Other effects which also contribute
to the shift are briefly discussed. We provide approximate analytic expressions
for the non-linear shift including a brief discussion of biased tracers and
explain why reconstruction should entirely reverse the shift. Our expressions
and findings are in agreement with simulation results, and confirm that
non-linear shifts should not be problematic for next-generation BAO
measurements.Comment: 10 pages, replaced with version accepted by Phys. Rev.
Bootstrap-Based Inference for Cube Root Asymptotics
This paper proposes a valid bootstrap-based distributional approximation for
M-estimators exhibiting a Chernoff (1964)-type limiting distribution. For
estimators of this kind, the standard nonparametric bootstrap is inconsistent.
The method proposed herein is based on the nonparametric bootstrap, but
restores consistency by altering the shape of the criterion function defining
the estimator whose distribution we seek to approximate. This modification
leads to a generic and easy-to-implement resampling method for inference that
is conceptually distinct from other available distributional approximations. We
illustrate the applicability of our results with four examples in econometrics
and machine learning
Inference in Linear Regression Models with Many Covariates and Heteroskedasticity
The linear regression model is widely used in empirical work in Economics,
Statistics, and many other disciplines. Researchers often include many
covariates in their linear model specification in an attempt to control for
confounders. We give inference methods that allow for many covariates and
heteroskedasticity. Our results are obtained using high-dimensional
approximations, where the number of included covariates are allowed to grow as
fast as the sample size. We find that all of the usual versions of Eicker-White
heteroskedasticity consistent standard error estimators for linear models are
inconsistent under this asymptotics. We then propose a new heteroskedasticity
consistent standard error formula that is fully automatic and robust to both
(conditional)\ heteroskedasticity of unknown form and the inclusion of possibly
many covariates. We apply our findings to three settings: parametric linear
models with many covariates, linear panel models with many fixed effects, and
semiparametric semi-linear models with many technical regressors. Simulation
evidence consistent with our theoretical results is also provided. The proposed
methods are also illustrated with an empirical application
Dynamic allometry in coastal overwash morphology
Allometry refers to a physical principle in which geometric (and/or metabolic) characteristics of an object or organism are correlated to its size. Allometric scaling relationships typically manifest as power laws. In geomorphic contexts, scaling relationships are a quantitative signature of organization, structure, or regularity in a landscape, even if the mechanistic processes responsible for creating such a pattern are unclear. Despite the ubiquity and variety of scaling relationships in physical landscapes, the emergence and development of these relationships tend to be difficult to observe - either because the spatial and/or temporal scales over which they evolve are so great or because the conditions that drive them are so dangerous (e.g. an extreme hazard event). Here, we use a physical experiment to examine dynamic allometry in overwash morphology along a model coastal barrier. We document the emergence of a canonical scaling law for length versus area in overwash deposits (washover). Comparing the experimental features, formed during a single forcing event, to 5 decades of change in real washover morphology from the Ria Formosa barrier system, in southern Portugal, we find differences between patterns of morphometric change at the event scale versus longer timescales. Our results may help inform and test process-based coastal morphodynamic models, which typically use statistical distributions and scaling laws to underpin empirical or semi-empirical parameters at fundamental levels of model architecture. More broadly, this work dovetails with theory for landscape evolution more commonly associated with fluvial and alluvial terrain, offering new evidence from a coastal setting that a landscape may reflect characteristics associated with an equilibrium or steady-state condition even when features within that landscape do not.Funding Agency
NERC Natural Environment Research Council
NE/N015665/2
Leverhulme Trust
RPG-2018-282info:eu-repo/semantics/publishedVersio
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
A Random Attention Model
This paper illustrates how one can deduce preference from observed choices
when attention is not only limited but also random. In contrast to earlier
approaches, we introduce a Random Attention Model (RAM) where we abstain from
any particular attention formation, and instead consider a large class of
nonparametric random attention rules. Our model imposes one intuitive
condition, termed Monotonic Attention, which captures the idea that each
consideration set competes for the decision-maker's attention. We then develop
revealed preference theory within RAM and obtain precise testable implications
for observable choice probabilities. Based on these theoretical findings, we
propose econometric methods for identification, estimation, and inference of
the decision maker's preferences. To illustrate the applicability of our
results and their concrete empirical content in specific settings, we also
develop revealed preference theory and accompanying econometric methods under
additional nonparametric assumptions on the consideration set for binary choice
problems. Finally, we provide general purpose software implementation of our
estimation and inference results, and showcase their performance using
simulations
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