Nonparametric Estimation of Repeated Densities with Heterogeneous Sample Sizes

Qiu, Jiaming; Dai, Xiongtao; Zhu, Zhengyuan

doi:10.1080/01621459.2022.2104728

Cited by 1 publication

(1 citation statement)

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“…Estimating density f i becomes particularly challenging when dealing with small sample sizes m i in each observation unit. To address this, a two-step approach is proposed by Qiu et al (2022) for cases with heterogeneous sample sizes. Firstly, the underlying process is estimated based on a subsample where each density is densely observed.…”

Section: Introductionmentioning

confidence: 99%

Elastic Analysis of Irregularly or Sparsely Sampled Curves

2022

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We propose regression models for curve-valued responses in two or more dimensions, where only the image but not the parametrization of the curves is of interest. Examples of such data are handwritten letters, movement paths or outlines of objects. In the square-root-velocity framework, a parametrization invariant distance for curves is obtained as the quotient space metric with respect to the action of re-parametrization, which is by isometries. With this special case in mind, we discuss the generalization of 'linear' regression to quotient metric spaces more generally, before illustrating the usefulness of our approach for curves modulo re-parametrization. We address the issue of sparsely or irregularly sampled curves by using splines for modeling smooth conditional mean curves. We test this model in simulations and apply it to human hippocampal outlines, obtained from Magnetic Resonance Imaging scans. Here we model how the shape of the irregularly sampled hippocampus is related to age, Alzheimer's disease and sex.

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Section: Introductionmentioning

confidence: 99%