46 research outputs found
Dynamic Modeling and Statistical Analysis of Event Times
This review article provides an overview of recent work in the modeling and
analysis of recurrent events arising in engineering, reliability, public
health, biomedicine and other areas. Recurrent event modeling possesses unique
facets making it different and more difficult to handle than single event
settings. For instance, the impact of an increasing number of event occurrences
needs to be taken into account, the effects of covariates should be considered,
potential association among the interevent times within a unit cannot be
ignored, and the effects of performed interventions after each event occurrence
need to be factored in. A recent general class of models for recurrent events
which simultaneously accommodates these aspects is described. Statistical
inference methods for this class of models are presented and illustrated
through applications to real data sets. Some existing open research problems
are described.Comment: Published at http://dx.doi.org/10.1214/088342306000000349 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Pranab Kumar Sen: Life and works
In this article, we describe briefly the highlights and various
accomplishments in the personal as well as the academic life of Professor
Pranab Kumar Sen.Comment: Published in at http://dx.doi.org/10.1214/193940307000000013 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
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
Estimating Load-Sharing Properties in a Dynamic Reliability System
An estimator for the load-share parameters in an equal load-share model is derived based on observing k-component parallel systems of identical components that have a continuous distribution function F (˙) and failure rate r (˙). In an equal load-share model, after the first of k components fails, failure rates for the remaining components change from r (t) to γ1r (t), then to γ2r (t) after the next failure, and so on. On the basis of observations on n independent and identical systems, a semiparametric estimator of the component baseline cumulative hazard function R = –log(1 – F) is presented, and its asymptotic limit process is established to be a Gaussian process. The effect of estimation of the load-share parameters is considered in the derivation of the limiting process. Potential applications can be found in diverse areas, including materials testing, software reliability, and power plant safety assessment
Classes of Multiple Decision Functions Strongly Controlling FWER and FDR
This paper provides two general classes of multiple decision functions where
each member of the first class strongly controls the family-wise error rate
(FWER), while each member of the second class strongly controls the false
discovery rate (FDR). These classes offer the possibility that an optimal
multiple decision function with respect to a pre-specified criterion, such as
the missed discovery rate (MDR), could be found within these classes. Such
multiple decision functions can be utilized in multiple testing, specifically,
but not limited to, the analysis of high-dimensional microarray data sets.Comment: 19 page