3,093 research outputs found
Analyzing two-stage experiments in the presence of interference
Two-stage randomization is a powerful design for estimating treatment effects
in the presence of interference; that is, when one individual's treatment
assignment affects another individual's outcomes. Our motivating example is a
two-stage randomized trial evaluating an intervention to reduce student
absenteeism in the School District of Philadelphia. In that experiment,
households with multiple students were first assigned to treatment or control;
then, in treated households, one student was randomly assigned to treatment.
Using this example, we highlight key considerations for analyzing two-stage
experiments in practice. Our first contribution is to address additional
complexities that arise when household sizes vary; in this case, researchers
must decide between assigning equal weight to households or equal weight to
individuals. We propose unbiased estimators for a broad class of individual-
and household-weighted estimands, with corresponding theoretical and estimated
variances. Our second contribution is to connect two common approaches for
analyzing two-stage designs: linear regression and randomization inference. We
show that, with suitably chosen standard errors, these two approaches yield
identical point and variance estimates, which is somewhat surprising given the
complex randomization scheme. Finally, we explore options for incorporating
covariates to improve precision. We confirm our analytic results via simulation
studies and apply these methods to the attendance study, finding substantively
meaningful spillover effects.Comment: Accepted for publication in the Journal of the American Statistical
Associatio
On the uniform convergence of random series in Skorohod space and representations of c\`{a}dl\`{a}g infinitely divisible processes
Let be independent random elements in the Skorohod space
of c\`{a}dl\`{a}g functions taking values in a separable Banach space . Let
. We show that if converges in finite dimensional
distributions to a c\`{a}dl\`{a}g process, then converges a.s.
pathwise uniformly over , for some . This result
extends the It\^{o}-Nisio theorem to the space , which is
surprisingly lacking in the literature even for . The main difficulties of
dealing with in this context are its nonseparability under the
uniform norm and the discontinuity of addition under Skorohod's -topology.
We use this result to prove the uniform convergence of various series
representations of c\`{a}dl\`{a}g infinitely divisible processes. As a
consequence, we obtain explicit representations of the jump process, and of
related path functionals, in a general non-Markovian setting. Finally, we
illustrate our results on an example of stable processes. To this aim we obtain
new criteria for such processes to have c\`{a}dl\`{a}g modifications, which may
also be of independent interest.Comment: Published in at http://dx.doi.org/10.1214/12-AOP783 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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