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Consistent estimation of distributions with type II bias with applications in competing

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dc.contributor.author El Barmi, Hammou
dc.contributor.author Mukerjee, Hari
dc.date.accessioned 2012-06-21T15:34:43Z
dc.date.available 2012-06-21T15:34:43Z
dc.date.issued 2004-02
dc.identifier.citation Barmi, 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.issn 0090-5364
dc.identifier.uri http://hdl.handle.net/10057/5208
dc.identifier.uri http://dx.doi.org/10.1214/aos/1079120136
dc.identifier.uri http://projecteuclid.org/euclid.aos/1079120136
dc.description Open access
dc.description.abstract A 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.iso en_US en_US
dc.publisher Institute of Mathematical Statistics en_US
dc.relation.ispartofseries The Annals of Statistics;v.32 no.1
dc.subject Type II bias en_US
dc.subject Estimation
dc.subject Weak convergence
dc.subject Cumulative incidence functions
dc.subject Hypothesis testing
dc.subject Confidence bands
dc.title Consistent estimation of distributions with type II bias with applications in competing en_US
dc.type Article en_US
dc.description.version Peer reviewed
dc.rights.holder Copyright Institute of Mathematical Statistics 2004

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