Random censoring in set-indexed survival analysis

Ivanoff, B. Gail; Merzbach, Ely

doi:10.1214/aoap/1031863176

Cited by 13 publications

(34 citation statements)

References 14 publications

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“…Lemma 4.5) and (μ n (A) −μ(A)) → P 0 for every A ∈ B, (15) → P 0 by the exact same reasoning as for equation (29) in [2], while (18) …”

Section: Remark 47mentioning

confidence: 75%

“…Before moving on to measurable random sets, we should note that although we are restricting ourselves to a compact set T , all of the definitions and developments throughout this work can easily be expanded to a non-compact space using the structure found in Definition 2.1 of [2] (i.e., there exists an increasing sequence of compact sets (K n ) such that…”

Section: Lemma 24 For Every T ∈ T Both a T And E T Are D-closedmentioning

confidence: 99%

“…For T = [0, 1] 2 , there is a (0, 1]-valued random variable C such that ξ = [0, C ] 2 and so S = {[0, w] 2 : 0 < w ≤ 1}. This is a common censoring mechanism in medical studies involving two observations Y 1 and Y 2 on each test subject.…”

Section: Ordered Censoringmentioning

confidence: 99%

“…In recent papers, [1][2][3], the problem of survival analysis on a general partially ordered complete separable metric space was approached from the point of view of set-indexed martingales (cf. [4]).…”

Section: Introductionmentioning

confidence: 99%

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Estimation of a distribution under generalized censoring

Carabarín-Aguirre

Ivanoff

2010

Journal of Multivariate Analysis

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a b s t r a c tThis paper focuses on the problem of the estimation of a distribution on an arbitrary complete separable metric space when the data points are subject to censoring by a general class of random sets. If the censoring mechanism is either totally observable or totally ordered, a reverse probability estimator may be defined in this very general framework. Functional central limit theorems are proven for the estimator when the underlying space is Euclidean. Applications are discussed, and the validity of bootstrap methods is established in each case.

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“…Lemma 4.5) and (μ n (A) −μ(A)) → P 0 for every A ∈ B, (15) → P 0 by the exact same reasoning as for equation (29) in [2], while (18) …”

Section: Remark 47mentioning

confidence: 75%

Section: Lemma 24 For Every T ∈ T Both a T And E T Are D-closedmentioning

confidence: 99%

Section: Ordered Censoringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of a distribution under generalized censoring

Carabarín-Aguirre

Ivanoff

2010

Journal of Multivariate Analysis

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“…The frame of set-indexed processes is not only a new step of generalization of multiparameter processes, but it provides a real tool in modeling (e. g. [13]). Then a set-indexed extension of fractional Brownian motion is hoped to provide a powerful model for multidimensional phenomena.…”

Section: Introductionmentioning

confidence: 99%

A Set-indexed Fractional Brownian Motion

Herbin

Merzbach

2006

J Theor Probab

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We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed Brownian motion, when the condition of independance is relaxed. Relations with the Lévy fractional Brownian motion and with the fractional Brownian sheet are studied. We prove stationarity of the increments and a property of self-similarity with respect to the action of solid motions. Moreover, we show that there no "really nice" set indexed fractional Brownian motion other than set-indexed Brownian motion. Finally, behavior of the set-indexed fractional Brownian motion along increasing paths is analysed.

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Filtering of Multiparameter Processes: Theory and Applications

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Random censoring in set-indexed survival analysis

Cited by 13 publications

References 14 publications

Estimation of a distribution under generalized censoring

Estimation of a distribution under generalized censoring

A Set-indexed Fractional Brownian Motion

Filtering of Multiparameter Processes: Theory and Applications

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