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dc.contributor.authorEl Barmi, Hammou
dc.contributor.authorMukerjee, Hari
dc.date.accessioned2012-06-21T15:34:43Z
dc.date.available2012-06-21T15:34:43Z
dc.date.issued2004-02
dc.identifier.citationBarmi, H. E. and H. Mukerjee (2004). "Consistent Estimation of Distributions with Type II Bias with Applications in Competing Risks Problems." The Annals of Statistics 32(1): 245-267.en_US
dc.identifier.issn0090-5364
dc.identifier.urihttp://hdl.handle.net/10057/5208
dc.identifier.urihttp://dx.doi.org/10.1214/aos/1079120136
dc.identifier.urihttp://projecteuclid.org/euclid.aos/1079120136
dc.descriptionOpen access
dc.description.abstractA random variable X is symmetric about 0 if X and -X have the same distribution. There is a large literature on the estimation of a distribution function (DF) under the symmetry restriction and tests for checking this symmetry assumption. Often the alternative describes some notion of skewness or one-sided bias. Various notions can be described by an orderingo f the distributionso f X and -X. One such importanto rderingi s that P(O < X < x) - P(-x < X < 0) is increasing in x > 0. The distribution of X is said to have a Type II positive bias in this case. If X has a density f, then this corresponds to the density ordering f(-x) < f(x) for x > 0. It is known that the nonparametricm aximum likelihood estimator (NPMLE) of the DF under this restriction is inconsistent. We provide a projection-type estimator that is similar to a consistent estimator of two DFs under uniform stochastic ordering, where the NPMLE also fails to be consistent. The weak convergence of the estimator has been derived which can be used for testing the null hypothesis of symmetry against this one-sided alternative. It also turns out that the same procedure can be used to estimate two cumulative incidence functions in a competing risks problem under the restriction that the cause specific hazard rates are ordered. We also provide some real life examples.en_US
dc.language.isoen_USen_US
dc.publisherInstitute of Mathematical Statisticsen_US
dc.relation.ispartofseriesThe Annals of Statistics;v.32 no.1
dc.subjectType II biasen_US
dc.subjectEstimation
dc.subjectWeak convergence
dc.subjectCumulative incidence functions
dc.subjectHypothesis testing
dc.subjectConfidence bands
dc.titleConsistent estimation of distributions with type II bias with applications in competingen_US
dc.typeArticleen_US
dc.description.versionPeer reviewed
dc.rights.holderCopyright Institute of Mathematical Statistics 2004


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