SiZer for exploration of structures in curves. In the use of smoothing methods in data analysis, an important question is which observed features are “really there,” as opposed to being spurious sampling artifacts. An approach is described based on scale-space ideas originally developed in the computer vision literature. Assessment of Significant ZERo crossings of derivatives results in the SiZer map, a graphical device for display of significance of features with respect to both location and scale. Here “scale” means “level of resolution”; that is, “bandwidth.”

References in zbMATH (referenced in 70 articles , 1 standard article )

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  1. Telschow, Fabian J. E.; Schwartzman, Armin: Simultaneous confidence bands for functional data using the Gaussian kinematic formula (2022)
  2. Chandler, Gabriel; Polonik, Wolfgang: Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications (2021)
  3. Pewsey, Arthur; García-Portugués, Eduardo: Recent advances in directional statistics (2021)
  4. Rattihalli, R. N.; Patil, S. B.: Data dependent asymmetric kernels for estimating the density function (2021)
  5. Killick, Rebecca; Knight, Marina I.; Nason, Guy P.; Eckley, Idris A.: The local partial autocorrelation function and some applications (2020)
  6. Vogt, Michael; Linton, Oliver: Multiscale clustering of nonparametric regression curves (2020)
  7. Ye, Zi; Hooker, Giles; Ellner, Stephen P.: The Jensen effect and functional single index models: estimating the ecological implications of nonlinear reaction norms (2020)
  8. Ameijeiras-Alonso, Jose; Crujeiras, Rosa M.; Rodríguez-Casal, Alberto: Mode testing, critical bandwidth and excess mass (2019)
  9. Eckle, Konstantin; Bissantz, Nicolai; Dette, Holger; Proksch, Katharina; Einecke, Sabrina: Multiscale inference for a multivariate density with applications to X-ray astronomy (2018)
  10. Vuollo, Ville; Holmström, Lasse: A scale space approach for exploring structure in spherical data (2018)
  11. Jang, Dongik; Oh, Hee-Seok; Naveau, Philippe: Identifying local smoothness for spatially inhomogeneous functions (2017)
  12. Huckemann, Stephan; Kim, Kwang-Rae; Munk, Axel; Rehfeldt, Florian; Sommerfeld, Max; Weickert, Joachim; Wollnik, Carina: The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation (2016)
  13. Ma, Xuejun; He, Xiaoqun; Shi, Xiaokang: A variant of (K) nearest neighbor quantile regression (2016)
  14. Park, Cheolwoo; Jeon, Yongho; Kang, Kee-Hoon: An exploratory data analysis in scale-space for interval-valued data (2016)
  15. Huh, Jib; Park, Cheolwoo: Theoretical investigation of an exploratory approach for log-density in scale-space (2015)
  16. Pasanen, Leena; Holmström, Lasse: Bayesian scale space analysis of temporal changes in satellite images (2015)
  17. Frick, Klaus; Munk, Axel; Sieling, Hannes: Multiscale change point inference. With discussion and authors’ reply (2014)
  18. Zhang, Lingsong; Zhu, Zhengyuan; Marron, J. S.: Multiresolution anomaly detection method for fractional Gaussian noise (2014)
  19. Chacón, José E.; Duong, Tarn: Data-driven density derivative estimation, with applications to nonparametric clustering and bump hunting (2013)
  20. Heidenreich, Nils-Bastian; Schindler, Anja; Sperlich, Stefan: Bandwidth selection for kernel density estimation: a review of fully automatic selectors (2013)

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