737 research outputs found
Asymptotic Theory of Rerandomization in Treatment-Control Experiments
Although complete randomization ensures covariate balance on average, the
chance for observing significant differences between treatment and control
covariate distributions increases with many covariates. Rerandomization
discards randomizations that do not satisfy a predetermined covariate balance
criterion, generally resulting in better covariate balance and more precise
estimates of causal effects. Previous theory has derived finite sample theory
for rerandomization under the assumptions of equal treatment group sizes,
Gaussian covariate and outcome distributions, or additive causal effects, but
not for the general sampling distribution of the difference-in-means estimator
for the average causal effect. To supplement existing results, we develop
asymptotic theory for rerandomization without these assumptions, which reveals
a non-Gaussian asymptotic distribution for this estimator, specifically a
linear combination of a Gaussian random variable and a truncated Gaussian
random variable. This distribution follows because rerandomization affects only
the projection of potential outcomes onto the covariate space but does not
affect the corresponding orthogonal residuals. We also demonstrate that,
compared to complete randomization, rerandomization reduces the asymptotic
sampling variances and quantile ranges of the difference-in-means estimator.
Moreover, our work allows the construction of accurate large-sample confidence
intervals for the average causal effect, thereby revealing further advantages
of rerandomization over complete randomization
Chemical Self Assembly of Graphene Sheets
Chemically derived graphene sheets were found to self-assemble onto patterned
gold structures via electrostatic interactions between noncovalent functional
groups on GS and gold. This afforded regular arrays of single graphene sheets
on large substrates, characterized by scanning electron and Auger microscopy
imaging and Raman spectroscopy. Self assembly was used for the first time to
produce on-substrate and fully-suspended graphene electrical devices. Molecular
coatings on the GS were removed by high current electrical annealing, which
recovered the high electrical conductance and Dirac point of the GS. Molecular
sensors for highly sensitive gas detections are demonstrated with
self-assembled GS devices.Comment: Nano Research, in press, http://www.thenanoresearch.co
Sensitivity Analysis for Quantiles of Hidden Biases in Matched Observational Studies
In matched observational studies, the inferred causal conclusions pretending
that matching has taken into account all confounding can be sensitive to
unmeasured confounding. In such cases, a sensitivity analysis is often
conducted, which investigates whether the observed association between
treatment and outcome is due to effects caused by the treatment or it is due to
hidden confounding. In general, a sensitivity analysis tries to infer the
minimum amount of hidden biases needed in order to explain away the observed
association between treatment and outcome, assuming that the treatment has no
effect. If the needed bias is large, then the treatment is likely to have
significant effects. The Rosenbaum sensitivity analysis is a modern approach
for conducting sensitivity analysis for matched observational studies. It
investigates what magnitude the maximum of the hidden biases from all matched
sets needs to be in order to explain away the observed association, assuming
that the treatment has no effect. However, such a sensitivity analysis can be
overly conservative and pessimistic, especially when the investigators believe
that some matched sets may have exceptionally large hidden biases. In this
paper, we generalize Rosenbaum's framework to conduct sensitivity analysis on
quantiles of hidden biases from all matched sets, which are more robust than
the maximum. Moreover, we demonstrate that the proposed sensitivity analysis on
all quantiles of hidden biases is simultaneously valid and is thus a free lunch
added to the conventional sensitivity analysis. The proposed approach works for
general outcomes, general matched studies and general test statistics. Finally,
we demonstrate that the proposed sensitivity analysis also works for bounded
null hypotheses as long as the test statistic satisfies certain properties. An
R package implementing the proposed method is also available online
- …