Deconvolution When Classifying Noisy Data Involving Transformations

Carroll, Raymond J.; Delaigle, Aurore; Hall, Peter

doi:10.1080/01621459.2012.699793

Cited by 4 publications

(3 citation statements)

References 33 publications

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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%

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%

A deconvolution path for mixtures

Madrid-Padilla¹,

Polson²,

Scott³

2018

Electron. J. Statist.

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“…So there is a lot of interest in knowing whether the two types of clouds are different. The data have been previously described in Carroll et al (2012) and discussed recently in Serban et al (2013) and Xun et al (2013).…”

Section: Discussionmentioning

confidence: 99%

Significance tests for functional data with complex dependence structure

Staicu

Lahiri

Carroll

2015

Journal of Statistical Planning and Inference

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We propose an L2-norm based global testing procedure for the null hypothesis that multiple group mean functions are equal, for functional data with complex dependence structure. Specifically, we consider the setting of functional data with a multilevel structure of the form groups–clusters or subjects–units, where the unit-level profiles are spatially correlated within the cluster, and the cluster-level data are independent. Orthogonal series expansions are used to approximate the group mean functions and the test statistic is estimated using the basis coefficients. The asymptotic null distribution of the test statistic is developed, under mild regularity conditions. To our knowledge this is the first work that studies hypothesis testing, when data have such complex multilevel functional and spatial structure. Two small-sample alternatives, including a novel block bootstrap for functional data, are proposed, and their performance is examined in simulation studies. The paper concludes with an illustration of a motivating experiment.

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“…The data are described in detail by Carroll et al (2012), and the estimation of spectral backscatter uses the algorithm of Warren et al (2008, 2009), but applied to the observed data rather than the deconvolved data. Our main goal is to estimate the probability of high spectral backscatter at different wavelengths.…”

Section: Discussionmentioning

confidence: 99%

Multilevel Cross-Dependent Binary Longitudinal Data

2013

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We provide insights into new methodology for the analysis of multilevel binary data observed longitudinally, when the repeated longitudinal measurements are correlated. The proposed model is logistic functional regression conditioned on three latent processes describing the within- and between-variability, and describing the cross-dependence of the repeated longitudinal measurements. We estimate the model components without employing mixed-effects modeling but assuming an approximation to the logistic link function. The primary objectives of this paper are to highlight the challenges in the estimation of the model components, to compare two approximations to the logistic regression function, linear and exponential, and to discuss their advantages and limitations. The linear approximation is computationally efficient whereas the exponential approximation applies for rare events functional data. Our methods are inspired by and applied to a scientific experiment on spectral backscatter from long range infrared light detection and ranging (LIDAR) data. The models are general and relevant to many new binary functional data sets, with or without dependence between repeated functional measurements.

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Deconvolution When Classifying Noisy Data Involving Transformations

Cited by 4 publications

References 33 publications

A deconvolution path for mixtures

A deconvolution path for mixtures

Significance tests for functional data with complex dependence structure

Multilevel Cross-Dependent Binary Longitudinal Data

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