Deconvolution density estimation using penalized splines

A straight-forward solution to the deconvolution density estimation involves penalized splines. A priori information about shape of the densities is readily imposed; for example the estimates may be constrained to be unimodal or bimodal. With quadratic splines and uniform errors, a cube-root converg...

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 241; p. 106310
Main Authors Jing, Hanxiao, Meyer, Mary C., Sun, Jiayang
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2026
Subjects
Deconvolution
Density estimation
Measurement error
Splines
Density estimation
Deconvolution
Splines
Measurement error
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ISSN0378-3758
DOI10.1016/j.jspi.2025.106310

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Summary:A straight-forward solution to the deconvolution density estimation involves penalized splines. A priori information about shape of the densities is readily imposed; for example the estimates may be constrained to be unimodal or bimodal. With quadratic splines and uniform errors, a cube-root convergence rate is attained. Simulations show that the estimators perform well compared to kernel estimators in a variety of scenarios. •A penalized spline is used to estimate a unimodal or bimodal density.•Estimating a deconvolution density is appropriate when the measurements have errors.•For observed Y = X + Z, we estimate the density for X when the Z density is known.•For estimating a density with uniform errors, we obtain a cube root convergence rate.•Simulations show that the estimators perform well compared to the kernel estimator.
ISSN:0378-3758
DOI:10.1016/j.jspi.2025.106310