5,425 research outputs found
Identifiability of Subgroup Causal Effects in Randomized Experiments with Nonignorable Missing Covariates
Although randomized experiments are widely regarded as the gold standard for
estimating causal effects, missing data of the pretreatment covariates makes it
challenging to estimate the subgroup causal effects. When the missing data
mechanism of the covariates is nonignorable, the parameters of interest are
generally not pointly identifiable, and we can only get bounds for the
parameters of interest, which may be too wide for practical use. In some real
cases, we have prior knowledge that some restrictions may be plausible. We show
the identifiability of the causal effects and joint distributions for four
interpretable missing data mechanisms, and evaluate the performance of the
statistical inference via simulation studies. One application of our methods to
a real data set from a randomized clinical trial shows that one of the
nonignorable missing data mechanisms fits better than the ignorable missing
data mechanism, and the results conform to the study's original expert
opinions. We also illustrate the potential applications of our methods to
observational studies using a data set from a job-training program.Comment: Statistics in Medicine (2014
Identifiability of Normal and Normal Mixture Models With Nonignorable Missing Data
Missing data problems arise in many applied research studies. They may
jeopardize statistical inference of the model of interest, if the missing
mechanism is nonignorable, that is, the missing mechanism depends on the
missing values themselves even conditional on the observed data. With a
nonignorable missing mechanism, the model of interest is often not identifiable
without imposing further assumptions. We find that even if the missing
mechanism has a known parametric form, the model is not identifiable without
specifying a parametric outcome distribution. Although it is fundamental for
valid statistical inference, identifiability under nonignorable missing
mechanisms is not established for many commonly-used models. In this paper, we
first demonstrate identifiability of the normal distribution under monotone
missing mechanisms. We then extend it to the normal mixture and mixture
models with non-monotone missing mechanisms. We discover that models under the
Logistic missing mechanism are less identifiable than those under the Probit
missing mechanism. We give necessary and sufficient conditions for
identifiability of models under the Logistic missing mechanism, which sometimes
can be checked in real data analysis. We illustrate our methods using a series
of simulations, and apply them to a real-life dataset
Qualitative Evaluation of Associations by the Transitivity of the Association Signs
We say that the signs of association measures among three variables {X, Y, Z}
are transitive if a positive association measure between the variable X and the
intermediate variable Y and further a positive association measure between Y
and the endpoint variable Z imply a positive association measure between X and
Z. We introduce four association measures with different stringencies, and
discuss conditions for the transitivity of the signs of these association
measures. When the variables follow exponential family distributions, the
conditions become simpler and more interpretable. Applying our results to two
data sets from an observational study and a randomized experiment, we
demonstrate that the results can help us to draw conclusions about the signs of
the association measures between X and Z based only on two separate studies
about {X, Y} and {Y, Z}.Comment: Statistica Sinica 201
Statistical Analysis of a Posteriori Channel and Noise Distribution Based on HARQ Feedback
In response to a comment on one of our manuscript, this work studies the
posterior channel and noise distributions conditioned on the NACKs and ACKs of
all previous transmissions in HARQ system with statistical approaches. Our main
result is that, unless the coherence interval (time or frequency) is large as
in block-fading assumption, the posterior distribution of the channel and noise
either remains almost identical to the prior distribution, or it mostly follows
the same class of distribution as the prior one. In the latter case, the
difference between the posterior and prior distribution can be modeled as some
parameter mismatch, which has little impact on certain type of applications.Comment: 15 pages, 2 figures, 4 table
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