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Abstract Proliferation of high‐resolution imaging data in recent years has led to substantial improvements in the two popular approaches for analyzing shapes of data objects based on landmarks and/or continuous curves. We provide an expository account of elastic shape analysis of parametric planar curves representing shapes of two‐dimensional (2D) objects by discussing its differences, and its commonalities, to the landmark‐based approach. Particular attention is accorded to the role of reparameterization of a curve, which in addition to rotation, scaling and translation, represents an important shape‐preserving transformation of a curve. The transition to the curve‐based approach moves the mathematical setting of shape analysis from finite‐dimensional non‐Euclidean spaces to infinite‐dimensional ones. We discuss some of the challenges associated with the infinite‐dimensionality of the shape space, and illustrate the use of geometry‐based methods in the computation of intrinsic statistical summaries and in the definition of statistical models on a 2D imaging dataset consisting of mouse vertebrae. We conclude with an overview of the current state‐of‐the‐art in the field. This article is categorized under: Image and Spatial Data < Data: Types and StructureComputational Mathematics < Applications of Computational Statistics
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This content will become publicly available on March 7, 2026
Empirical Likelihood in Functional Data Analysis
Functional data analysis (FDA) studies data that include infinite-dimensional functions or objects, generalizing traditional univariate or multivariate observations from each study unit. Among inferential approaches without parametric assumptions, empirical likelihood (EL) offers a principled method in that it extends the framework of parametric likelihood ratio–based inference via the nonparametric likelihood. There has been increasing use of EL in FDA due to its many favorable properties, including self-normalization and the data-driven shape of confidence regions. This article presents a review of EL approaches in FDA, starting with finite-dimensional features, then covering infinite-dimensional features. We contrast smooth and nonsmooth frameworks in FDA and show how EL has been incorporated into both of them. The article concludes with a discussion of some future research directions, including the possibility of applying EL to conformal inference.
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- Award ID(s):
- 2112938
- PAR ID:
- 10627798
- Publisher / Repository:
- Annual Reviews
- Date Published:
- Journal Name:
- Annual Review of Statistics and Its Application
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2326-8298
- Page Range / eLocation ID:
- 425 to 448
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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