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  4. Smoothness-Penalized Deconvolution: Rates of Convergence, Choice of Tuning Parameter, and Inference

Smoothness-Penalized Deconvolution: Rates of Convergence, Choice of Tuning Parameter, and Inference

File(s)
Kent_cornellgrad_0058F_14041.pdf (2.53 MB)
Permanent Link(s)
http://doi.org/10.7298/ckee-7845
https://hdl.handle.net/1813/115698
Collections
Cornell Theses and Dissertations
Author
Kent, David
Abstract

This work addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the contaminated observations and minimizes a reconstruction error penalized by an integrated squared m-th derivative. Theory for deconvolution has mainly focused on kernel- or wavelet-based techniques, but other methods including spline-based techniques and this smoothness-penalized estimator have been found to outperform kernel methods in simulation studies. This work fills in some of the gaps in theory by proving rates of convergence for the smoothness-penalized estimator and its spline approximant. We contribute to the practical use of the estimator by developing an unbiased estimator of its risk, along with a method for using that estimated risk to choose the tuning parameter; this outperforms the SURE-based tuning parameter method that has been proposed for a similar estimator. Finally, we develop methods for constructing bias-corrected pointwise confidence intervals and assess the coverage properties in a simulation study, finding that they have uniformly lower coverage error than the naive normal-theory intervals.

Description
143 pages
Date Issued
2023-12
Keywords
cross-validation
•
deconvolution
•
density estimation
•
measurement error
•
nonparametric statistics
•
regularization
Committee Chair
Ruppert, David
Committee Member
Kato, Kengo
Loredo, Thomas
Degree Discipline
Statistics
Degree Name
Ph. D., Statistics
Degree Level
Doctor of Philosophy
Type
dissertation or thesis
Link(s) to Catalog Record
https://newcatalog.library.cornell.edu/catalog/16454749

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