3,941 research outputs found
Power-enhanced multiple decision functions controlling family-wise error and false discovery rates
Improved procedures, in terms of smaller missed discovery rates (MDR), for
performing multiple hypotheses testing with weak and strong control of the
family-wise error rate (FWER) or the false discovery rate (FDR) are developed
and studied. The improvement over existing procedures such as the \v{S}id\'ak
procedure for FWER control and the Benjamini--Hochberg (BH) procedure for FDR
control is achieved by exploiting possible differences in the powers of the
individual tests. Results signal the need to take into account the powers of
the individual tests and to have multiple hypotheses decision functions which
are not limited to simply using the individual -values, as is the case, for
example, with the \v{S}id\'ak, Bonferroni, or BH procedures. They also enhance
understanding of the role of the powers of individual tests, or more precisely
the receiver operating characteristic (ROC) functions of decision processes, in
the search for better multiple hypotheses testing procedures. A
decision-theoretic framework is utilized, and through auxiliary randomizers the
procedures could be used with discrete or mixed-type data or with rank-based
nonparametric tests. This is in contrast to existing -value based procedures
whose theoretical validity is contingent on each of these -value statistics
being stochastically equal to or greater than a standard uniform variable under
the null hypothesis. Proposed procedures are relevant in the analysis of
high-dimensional "large , small " data sets arising in the natural,
physical, medical, economic and social sciences, whose generation and creation
is accelerated by advances in high-throughput technology, notably, but not
limited to, microarray technology.Comment: Published in at http://dx.doi.org/10.1214/10-AOS844 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Asymptotically optimal sequential design for rank aggregation
A sequential design problem for rank aggregation is commonly encountered in psychology, politics, marketing, sports, etc. In this problem, a decision maker is responsible for ranking K items by sequentially collecting noisy pairwise comparisons from judges. The decision maker needs to choose a pair of items for comparison in each step, decide when to stop data collection, and make a final decision after stopping based on a sequential flow of information. Because of the complex ranking structure, existing sequential analysis methods are not suitable. In this paper, we formulate the problem under a Bayesian decision framework and propose sequential procedures that are asymptotically optimal. These procedures achieve asymptotic optimality by seeking a balance between exploration (i.e., finding the most indistinguishable pair of items) and exploitation (i.e., comparing the most indistinguishable pair based on the current information). New analytical tools are developed for proving the asymptotic results, combining advanced change of measure techniques for handling the level crossing of likelihood ratios and classic large deviation results for martingales, which are of separate theoretical interest in solving complex sequential design problems. A mirror-descent algorithm is developed for the computation of the proposed sequential procedures
- …