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Modeling Probability Density Functions as Data Objects

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  • Petersen, Alexander
  • Zhang, Chao
  • Kokoszka, Piotr

Abstract

Recent developments in the probabilistic and statistical analysis of probability density functions are reviewed. Density functions are treated as data objects for which suitable notions of the center of distribution and variability are discussed. Special attention is given to nonlinear methods that respect the constraints density functions must obey. Regression, time series and spatial models are discussed. The exposition is illustrated with data examples. A supplementary vignette contains expanded versions of data analyses with accompanying codes.

Suggested Citation

  • Petersen, Alexander & Zhang, Chao & Kokoszka, Piotr, 2022. "Modeling Probability Density Functions as Data Objects," Econometrics and Statistics, Elsevier, vol. 21(C), pages 159-178.
    • Handle: RePEc:eee:ecosta:v:21:y:2022:i:c:p:159-178
    DOI: 10.1016/j.ecosta.2021.04.004
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    8. Kokoszka, Piotr & Miao, Hong & Petersen, Alexander & Shang, Han Lin, 2019. "Forecasting of density functions with an application to cross-sectional and intraday returns," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1304-1317.
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    2. Yabu, Takuya, 2023. "On Discrete Probability Distributions to Grasp the Number of Samples in a Population," OSF Preprints yv24f, Center for Open Science.
    3. Ghodrati, Laya & Panaretos, Victor M., 2023. "Minimax rate for optimal transport regression between distributions," Statistics & Probability Letters, Elsevier, vol. 194(C).
    4. Thomas-Agnan, Christine & Simioni, Michel & Trinh, Thi-Huong, 2023. "Discrete and Smooth Scalar-on-Density Compositional Regression for Assessing the Impact of Climate Change on Rice Yield in Vietnam," TSE Working Papers 23-1410, Toulouse School of Economics (TSE), revised Apr 2024.

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