Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-20T15:29:38.388Z Has data issue: false hasContentIssue false
  • English
  • Français

INFLUENCE FUNCTIONS FOR DIMENSION REDUCTION METHODS

Part of: Multivariate analysis Parametric inference

Published online by Cambridge University Press:  30 October 2020

JODIE ANN SMITH Open the ORCID record for JODIE ANN SMITH [Opens in a new window]
JODIE ANN SMITH*
Affiliation:
School of Engineering and Mathematical Sciences, La Trobe University, Melbourne, VIC3086, Australia
*
e-mail: ja12smith@gmail.com
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'

Keywords

dimension reductioneigen-subspaceinfluence analysisinfluence functionsinfluential observationslinear discriminant analysisprincipal Hessian directionssliced inverse regression

MSC classification

Primary: 62F35: Robustness and adaptive procedures
Secondary: 62H12: Estimation 62H30: Classification and discrimination; cluster analysis
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021 , pp. 517 - 519
Check for updates
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Footnotes

Thesis submitted to La Trobe University in September 2019; degree approved on 25 February 2020; principal supervisor Luke Prendergast, co-supervisor Robert Staudte.

References

Bellman, R. E., Adaptive Control Processes (Princeton University Press, Princeton, NJ, 1961).CrossRefGoogle Scholar
Cook, R. D., Regression Graphics: Ideas for Studying Regressions through Graphics (John Wiley, New York, 1998).CrossRefGoogle Scholar
Fisher, R. A., ‘The use of multiple measurements in taxonomic problems’, Ann. Eugen. 7(2) (1936), 179–188.CrossRefGoogle Scholar
Friedman, J. H., ‘An overview of computational learning and function approximation’, From Statistics to Neural Networks. Theory and Pattern Recognition Applications (eds. Cherkassky, V., Friedman, J. H. and Wechsler, H.) (Springer, Berlin, 1994), 1–61.Google Scholar
Gather, U. and Becker, C., ‘The curse of dimensionality—a challenge for mathematical statistics’, Jahresber. Dtsch. Math.-Ver. 103(1) (2001), 19–36.Google Scholar
Hampel, F. R., ‘The influence curve and its role in robust estimation’, J. Amer. Statist. Assoc. 69 (1974), 383–393.CrossRefGoogle Scholar
Hilbert, M. and López, P., ‘The world’s technological capacity to store, communicate, and compute information’, Science 332 (2011), 60–65.CrossRefGoogle ScholarPubMed
Li, K. C., ‘Sliced inverse regression for dimension reduction’, J. Amer. Statist. Assoc. 86 (1991), 316–342. With comments and a rejoinder by the author.CrossRefGoogle Scholar
Li, K. C., ‘On principal Hessian directions for data visualization and dimension reduction: another application of Stein’s lemma’, J. Amer. Statist. Assoc. 87 (1992), 1025–1039.CrossRefGoogle Scholar
Prendergast, L. A. and Smith, J. A., ‘Sensitivity of principal Hessian direction analysis’, Electron. J. Stat. 1 (2007), 253–267.CrossRefGoogle Scholar
Prendergast, L. A. and Smith, J. A., ‘Influence functions for dimension reduction methods: an example influence study of principal Hessian direction analysis’, Scand. J. Stat. 37(4) (2009), 588–611.CrossRefGoogle Scholar
Prendergast, L. A. and Smith, J. A., ‘Influence functions for linear discriminant analysis: sensitivity analysis and efficient influence diagnostics’, Preprint, 2019, arXiv:1909.13479.Google Scholar