Nonparametric Density Estimation from Biased Data with Unknown Biasing Function

Lloyd, Chris J.; Jones, M. C.

doi:10.2307/2669470

Cited by 7 publications

(4 citation statements)

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“…Our semiparametric formulation allows us to think about density deconvolution in terms of sampling bias, in that our data are drawn from density g 0 when our target is f 0 (Lloyd & Jones, 2000). Sampling from g 0 is equivalent to drawing candidate observations from f 0 and then accepting each with a probability proportional to 1/ w 0 .…”

Section: Weighted Kernel Estimation For the Semiparametric Modelmentioning

confidence: 99%

Semiparametric Density Deconvolution

Hazelton¹,

Turlach²

2010

Scandinavian Journal of Statistics

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A new semiparametric method for density deconvolution is proposed, based on a model in which only the ratio of the unconvoluted to convoluted densities is specified parametrically. Deconvolution results from reweighting the terms in a standard kernel density estimator, where the weights are defined by the parametric density ratio. We propose that in practice, the density ratio be modelled on the log-scale as a cubic spline with a fixed number of knots. Parameter estimation is based on maximization of a type of semiparametric likelihood. The resulting asymptotic properties for our deconvolution estimator mirror the convergence rates in standard density estimation without measurement error when attention is restricted to our semiparametric class of densities. Furthermore, numerical studies indicate that for practical sample sizes our weighted kernel estimator can provide better results than the classical non-parametric kernel estimator for a range of densities outside the specified semiparametric class. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.

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Section: Weighted Kernel Estimation For the Semiparametric Modelmentioning

confidence: 99%

Semiparametric Density Deconvolution

Hazelton¹,

Turlach²

2010

Scandinavian Journal of Statistics

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“…The overlap T ∩ T ′ provides some information about w and hence allows both f and w to be estimable nonparametrically in the range of T ∩ T ′ . See Lloyd and Jones [12], Wang and Sun [25], for more information on nonparametric estimates of f and w, based on two biased samples.…”

Section: Modelmentioning

confidence: 99%

Sieve estimates for biased survival data

Sun¹,

Wang²

2006

Institute of Mathematical Statistics Lecture Notes - Monograph Series

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In studies involving lifetimes, observed survival times are frequently censored and possibly subject to biased sampling. In this paper, we model survival times under biased sampling (a.k.a., biased survival data) by a semi-parametric model, in which the selection function $w(t)$ (that leads to the biased sampling) is specified up to an unknown finite dimensional parameter $\theta$, while the density function $f(t)$ of the survival times is assumed only to be smooth. Under this model, two estimators are derived to estimate the density function $f$, and a pseudo maximum likelihood estimation procedure is developed to estimate $\theta$. The identifiability of the estimation problem is discussed and the performance of the new estimators is illustrated via both simulation studies and a real data application.Comment: Published at http://dx.doi.org/10.1214/074921706000000644 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

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“…Simpler model-based approaches to analysis of ascertained data have been described previously. Rosenbaum (1987) described sampling weights modeled as a function of data descriptive of class/stratum features; Reilly, Gelman, and Katz (2001) used a similar approach applied to a time series of weekly political polling data; and Lloyd and Jones (2000) corrected for sampling bias in nonparametric density estimation using two samples from the population, both biased by the same function.…”

Section: Models and Notationmentioning

confidence: 99%

Population-Calibrated Gene Characterization

Iversen

Chen

2005

Journal of the American Statistical Association

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Phenotypic characterization of rare disease genes poses a significant statistical challenge, but the need to do so is clear. Clinical management of patients carrying a disease gene depends crucially on an accurate characterization of the genetically predisposed disease, including its likelihood of occurrence among mutation carriers, natural history, and response to treatment. We propose a formal yet practical method for controlling for bias due to ignoring ascertainment, defined as the sampling mechanism, when quantifying the association between genotype and disease using data on high-risk families. The approach is more statistically efficient than conditioning on the variables used in sampling. In it, the likelihood is adjusted by a factor that is a function of sampling weights in strata defined by those variables. It requires that these variables and the sampling probabilities in the strata they define either are known or can be estimated. The latter requires a second, population-based dataset. As an example, we derive ascertainment-corrected estimates of penetrance for the breast cancer susceptibility genes BRCA1 and BRCA2. The Bayesian analysis that we use incorporates a modified segregation model and prior data on penetrance derived from the literature. Markov chain Monte Carlo methods are used for inference.

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Nonparametric Density Estimation from Biased Data with Unknown Biasing Function

Cited by 7 publications

References 0 publications

Semiparametric Density Deconvolution

Semiparametric Density Deconvolution

Sieve estimates for biased survival data

Population-Calibrated Gene Characterization

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