Parametrically Assisted Nonparametric Estimation of a Density in the Deconvolution Problem

Delaigle, Aurore; Hall, Peter

doi:10.1080/01621459.2013.857611

Cited by 7 publications

(6 citation statements)

References 29 publications

(44 reference statements)

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“…Finally, we note the work by Carroll and Hall (1988); Stefanski and Carroll (1990); Zhang (1990); Fan (1991); Fan and Koo (2002); Hall et al (2007); Carroll et al (2012); Delaigle and Hall (2014), among others, who considered kernel estimators. Their idea is motivated by (1) after taking the Fourier transform of the corresponding convolution of densities, then solving for the unknown mixing density using kernel approximations for the Fourier transform of the true marginal density.…”

Section: Connections With Previous Workmentioning

confidence: 87%

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A deconvolution path for mixtures

Madrid-Padilla¹,

Polson²,

Scott³

2018

Electron. J. Statist.

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We propose a class of estimators for deconvolution in mixture models based on a simple two-step "bin-and-smooth" procedure applied to histogram counts. The method is both statistically and computationally efficient: by exploiting recent advances in convex optimization, we are able to provide a full deconvolution path that shows the estimate for the mixing distribution across a range of plausible degrees of smoothness, at far less cost than a full Bayesian analysis. This enables practitioners to conduct a sensitivity analysis with minimal effort. This is especially important for applied data analysis, given the ill-posed nature of the deconvolution problem. Our results establish the favorable theoretical properties of our estimator and show that it offers state-of-the-art performance when compared to benchmark methods across a range of scenarios.

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Section: Connections With Previous Workmentioning

confidence: 87%

“…Yet the estimation of f 0 continues to pose both theoretical and practical challenges, making it an active area of statistical research (e.g. Delaigle and Hall, 2014;Efron, 2016).…”

Section: Introductionmentioning

confidence: 99%

A deconvolution path for mixtures

Madrid-Padilla¹,

Polson²,

Scott³

2018

Electron. J. Statist.

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“…There is an extensive statistics literature addressing the additive deconvolution problem 14 . A common set of deconvolution methods are kernel-based approaches, such as those relying on Fourier transforms [15][16][17][18][19][20][21] , which use the fact that in Fourier space, a deconvolution is simply the product of two functions. Two problems arise from such methods that limit their applicability in practical cases.…”

Section: Introductionmentioning

confidence: 99%

Single-cell Bayesian deconvolution

Torregrosa

Oriola

Trivedi

et al. 2022

Preprint

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Flow cytometry enables monitoring protein abundance and activity at the single-cell level in a high-throughput manner, through the use of fluorescent labeling. Given the significant levels of autofluorescence emitted by cells at the spectral ranges used by this technique, removing the corresponding background signal is necessary for a correct assessment of cellular biochemistry. Existing methods of autofluorescence removal usually require dedicated monitoring resources, such as additional fluorescence channels or laser sources, which are costly and not universally accessible. Here, we have developed a computational method that enables autofluorescence subtraction without requiring dedicated measurement resources. The method uses a non-parametric Bayesian approach to deconvolve the target signal distribution from independent measurements of labeled and unlabeled cells readily available in a typical experiment. The distributions are approximated by mixtures of gamma functions, and the target distribution is obtained by sampling the posterior distribution using Markov chain Monte Carlo and nested sampling approaches. We tested the method systematically using synthetic data, and validated it using experimental data from mouse embryonic stem cells.

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“…Although it has been shown by Fan (1992) that nonparametric deconvolution with normal errors can be as good as the kernel density estimate based on uncontaminated data if the noise level decreases as sample size increases, an accelerated denconvolution is still much desirable. Recently Delaigle and Hall (2014) proposed an improved kernel method uponf F to speed up the convergence assisted by a "close to being correct" parametric guess of f . The assumption of a known error density g was discussed by Horowitz and Markatou (1996), Efromovich (1997Efromovich ( , 1999, and Neumann (1997).…”

Section: Introductionmentioning

confidence: 99%

Fast Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein Polynomial

Guan¹

2021

STAT SINICA

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A new maximum approximate likelihood method for deconvoluting a continuous density on a finite interval in additive measurement error models with known error distribution using the approximate Bernstein polynomial model, a finite mixture of specific beta distributions, is proposed. The change-point detection method is used to choose an optimal model degree. Based on a contaminated sample of size n, under an assumption which is satisfied, among others, by the generalized normal error distribution, the optimal rate of convergence of the mean integrated squared error is proved to be O(n −1+5/k log n) if the underlying unknown density admits an approximate Bernstein polynomial model of degree m within χ 2-divergence of order O(m −k) with k > 5. Simulation shows that the small sample performance of the proposed estimator is better than the deconvolution kernel density estimator. The proposed method is illustrated by a real data application.

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Parametrically Assisted Nonparametric Estimation of a Density in the Deconvolution Problem

Cited by 7 publications

References 29 publications

A deconvolution path for mixtures

A deconvolution path for mixtures

Single-cell Bayesian deconvolution

Fast Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein Polynomial

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