Test statistics are often strongly dependent in large-scale multiple testing
applications. Most corrections for multiplicity are unduly conservative for
correlated test statistics, resulting in a loss of power to detect true
positives. We show that the Westfall--Young permutation method has
asymptotically optimal power for a broad class of testing problems with a
block-dependence and sparsity structure among the tests, when the number of
tests tends to infinity.
We consider the problem of learning causal information between random
variables in DAGs when allowing arbitrarily many latent and selection
variables. The FCI algorithm (Spirtes et al., 1999) has been explicitly
designed to infer conditional independence and causal information in such
settings. However, FCI is computationally infeasible for large graphs. We
therefore propose a new algorithm, the RFCI algorithm, which is much faster
than FCI. In some situations the output of RFCI is slightly less informative,
in particular with respect to conditional independence information.
We consider variable selection in high-dimensional linear models where the
number of covariates greatly exceeds the sample size. We introduce the new
concept of partial faithfulness and use it to infer associations between the
covariates and the response.
We consider variable selection in high-dimensional linear models where the
number of covariates greatly exceeds the sample size. We introduce the new
concept of partial faithfulness and use it to infer associations between the
covariates and the response.
New methods and theory have recently been developed to nonparametrically
estimate cumulative incidence functions for competing risks survival data
subject to current status censoring. In particular, the limiting distribution
of the nonparametric maximum likelihood estimator (MLE) and a simplified "naive
estimator" have been established under certain smoothness conditions. In this
paper, we establish the large-sample behavior of these estimators in two
additional models, namely when the observation time distribution has finite
discrete support and when the observation times are grouped.
We assume that we have observational data generated from an unknown
underlying directed acyclic graph (DAG) model. A DAG is typically not
identifiable from observational data, but it is possible to consistently
estimate the equivalence class of a DAG. Moreover, for any given DAG, causal
effects can be estimated using intervention calculus. In this paper, we combine
these two parts. For each DAG in the estimated equivalence class, we use
intervention calculus to estimate the causal effects of the covariates on the
response.