Ranked Set Sampling with Size-Biased Probability of Selection

Muttlak, Hassen A.; McDonald, Lyman L.

doi:10.2307/2531448

Cited by 50 publications

(28 citation statements)

References 4 publications

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“…Linear boundary correction is used in Fig. 7 on the length-biased shrub width data of Muttlak and McDonald (1990); it is compared there with the truncated estimator used by Jones (1991) (n =46, h =0.23). It is encouraging to note that linear correction brings the estimate down near zero, while in Fig.…”

Section: Examples Of Linear Correctionmentioning

confidence: 99%

Simple boundary correction for kernel density estimation

1993

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If a probability density function has bounded support, kernel density estimates often overspill the boundaries and are consequently especially biased at and near these edges. In this paper, we consider the alleviation of this boundary problem. A simple unified framework is provided which covers a number of straightforward methods and allows for their comparison: 'generalized jackknifing' generates a variety of simple boundary kernel formulae. A well-known method of Rice (1984) is a special case. A popular linear correction method is another: it has close connections with the boundary properties of local linear fitting (Fan and Gijbels, 1992). Links with the 'optimal' boundary kernels of M011er (1991) are investigated. Novel boundary kernels involving kernel derivatives and generalized reflection arise too. In comparisons, various generalized jackknifing methods perform rather similarly, so this, together with its existing popularity, make linear correction as good a method as any. In an as yet unsuccessful attempt to improve on generalized jackknifing, a variety of alternative approaches is considered. A further contribution is to consider generalized jackknife boundary correction for density derivative estimation. En route to all this, a natural analogue of local polynomial regression for density estimation is defined and discussed.

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Section: Examples Of Linear Correctionmentioning

confidence: 99%

Simple boundary correction for kernel density estimation

1993

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“…In this subsection, we analyze three datasets, namely (i) a shrub dataset of Muttlak and McDonald (1990) for size-biased data, (ii) a dementia study carried out by Canadian Study of Health and Aging, and (iii) South Wales Nickel Refinery Study on nasal sinus. The first two sets of data correspond to length-/sizebiased data, while the last one involves case-cohort analysis and its variants.…”

Section: Real Examplesmentioning

confidence: 99%

“…Length/size-biased sampling has been recognized in statistics for decades in the studies of ecology (McFadden, 1962;Muttlak and McDonald, 1990), fiber length (Cox, 1969), and economic duration data (Kiefer, 1988). This kind of biased sampling arises when a positive-valued outcome variable is sampled with selection probability proportional to its size/survival time.…”

Section: Introductionmentioning

confidence: 99%

Accelerated failure time model under general biased sampling scheme: Table 1.

Kim

Sit

Ying

2016

Biostat

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SUMMARYRight-censored time-to-event data are sometimes observed from a (sub)cohort of patients whose survival times can be subject to outcome-dependent sampling schemes. In this paper, we propose a unified estimation method for semiparametric accelerated failure time models under general biased estimating schemes. The proposed estimator of the regression covariates is developed upon a bias-offsetting weighting scheme and is proved to be consistent and asymptotically normally distributed. Large sample properties for the estimator are also derived. Using rank-based monotone estimating functions for the regression parameters, we find that the estimating equations can be easily solved via convex optimization. The methods are confirmed through simulations and illustrated by application to real datasets on various sampling schemes including length-bias sampling, the case-cohort design and its variants.

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“…Shrub data. Muttlak & McDonald (1990) presented widths of 46 shrubs. Wang (1996) assumed that the probability of observing a shrub is proportional to the shrub's width, so that the sampling is length-biased.…”

Section: Wei Yann Tsaimentioning

confidence: 99%

Pseudo-partial likelihood for proportional hazards models with biased-sampling data

Tsai¹

2009

Biometrika

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SUMMARYWe obtain a pseudo-partial likelihood for proportional hazards models with biased-sampling data by embedding the biased-sampling data into left-truncated data. The log pseudo-partial likelihood of the biased-sampling data is the expectation of the log partial likelihood of the left-truncated data conditioned on the observed data. Asymptotic properties of the estimator that maximize the pseudo-partial likelihood are derived. Applications to length-biased data, biased samples with right censoring and proportional hazards models with missing covariates are discussed.

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Ranked Set Sampling with Size-Biased Probability of Selection

Cited by 50 publications

References 4 publications

Simple boundary correction for kernel density estimation

Simple boundary correction for kernel density estimation

Accelerated failure time model under general biased sampling scheme: Table 1.

Pseudo-partial likelihood for proportional hazards models with biased-sampling data

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