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Empirical Likelihood in Functional Data Analysis
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DOI：10.1146/annurev-statistics-112723-034225.png)
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Abstract
En 中文
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 selfnormalization 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.
Keywords:
dynamic correlation
functional linear models
functional ANOVA
pointwise and simultaneous inference
Journal
IF:
8.7
Papers:
211
Citations:
2.4K