89,917 research outputs found
Combining multiple observational data sources to estimate causal effects
The era of big data has witnessed an increasing availability of multiple data
sources for statistical analyses. We consider estimation of causal effects
combining big main data with unmeasured confounders and smaller validation data
with supplementary information on these confounders. Under the unconfoundedness
assumption with completely observed confounders, the smaller validation data
allow for constructing consistent estimators for causal effects, but the big
main data can only give error-prone estimators in general. However, by
leveraging the information in the big main data in a principled way, we can
improve the estimation efficiencies yet preserve the consistencies of the
initial estimators based solely on the validation data. Our framework applies
to asymptotically normal estimators, including the commonly-used regression
imputation, weighting, and matching estimators, and does not require a correct
specification of the model relating the unmeasured confounders to the observed
variables. We also propose appropriate bootstrap procedures, which makes our
method straightforward to implement using software routines for existing
estimators
Floquet second-order topological insulators from nonsymmorphic space-time symmetries
We propose a systematic way of constructing Floquet second-order topological
insulators (SOTIs) based on time-glide symmetry, a nonsymmorphic space-time
symmetry that is unique in Floquet systems. In particular, we are able to show
that the static enlarged Hamiltonian in the frequency domain acquires the
reflection symmetry, which is inherited from the time-glide symmetry of the
original system. As a consequence, one can construct a variety of time-glide
symmetric Floquet SOTIs using the knowledge of static SOTIs. Moreover, the
time-glide symmetry only needs to be implemented approximately in practice,
enhancing the prospects of experimental realizations. We consider two examples,
a 2D system in class AIII and a 3D system in class A, to illustrate our ideas,
and then present a general recipe for constructing Floquet SOTIs in all
symmetry classes.Comment: 5 pages + supplemental materia
Asymptotic causal inference with observational studies trimmed by the estimated propensity scores
Causal inference with observational studies often relies on the assumptions
of unconfoundedness and overlap of covariate distributions in different
treatment groups. The overlap assumption is violated when some units have
propensity scores close to 0 or 1, and therefore both practical and theoretical
researchers suggest dropping units with extreme estimated propensity scores.
However, existing trimming methods ignore the uncertainty in this design stage
and restrict inference only to the trimmed sample, due to the non-smoothness of
the trimming. We propose a smooth weighting, which approximates the existing
sample trimming but has better asymptotic properties. An advantage of the new
smoothly weighted estimator is its asymptotic linearity, which ensures that the
bootstrap can be used to make inference for the target population,
incorporating uncertainty arising from both the design and analysis stages. We
also extend the theory to the average treatment effect on the treated,
suggesting trimming samples with estimated propensity scores close to 1.Comment: 21 pages, 1 figures and 3 table
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