PL EN


2012 | 884 | 43-58
Article title

Statystyczne funkcje głębi we wstępnej analizie szeregu czasowego

Title variants
EN
Statistical Depth Functions in a Preliminary Analysis of Time Series
Languages of publication
PL
Abstracts
EN
In this paper I present selected applications of data depth-based statistical procedures for a preliminary analysis of time series. I focus our attention on simple methods induced by halfspace depth, regression depth and generalised band depth proposed by Pintado-Lopez and Romo. The Monte Carlo studies and empirical examples show our procedures to have good robustness properties.
Contributors
  • Uniwersytet Ekonomiczny w Krakowie, Katedra Statystyki, ul. Rakowicka 27, 31-510 Kraków, Poland
References
  • Bocian M., Kosiorowski D., Węgrzynkiewicz A., Zawadzki Z. [2012], {depthproc 1.0} – Pakiet środowiska R, https://r-forge.r-project.org/projects/depthproc/.
  • Demidenko E. [2004], Mixed Models – Theory and Applications, John Wiley & Sons, Hoboken, New Jersey.
  • Genton M.G., Lucas A. [2003], Comprehensive Definitions of Breakdown Points for Independent and Dependent Observations, „Journal of the Royal Statistical Society”, Series B 65(1).
  • Hampel F.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.A. [1986], Robust Statistics: The Approach Based on Influence Functions, John Wiley & Sons, New York.
  • Huber P., Ronchettii E.M. [2009], Robust Statistics, John Wiley & Sons, New York.
  • Kosiorowski D. [2007], O Odpornej Analizie Regresji w Ekonomii na Przykładzie Koncepcji Głębi Regresyjnej, „Przegląd Statystyczny” (1).
  • Kosiorowski D. [2008], Robust Classification and Clustering Based on the Projection Depth Function, red. P. Brito, Physica-Verlag, Heidelberg.
  • Kosiorowski D. [2009], Wybrane zagadnienia koncepcji głębi danych, Folia Oeconomica Cracoviensia, vol. XLIX–L.
  • Kosiorowski D. [2010a], Depth Based Procedures for Estimation ARMA and GARCH Models, red. Y. Lechevallier, G. Saporta, Proceedings of COMPSTAT’2010, 19th International Conference on Computational Statistics, Physica-Verlag.
  • Kosiorowski D. [2010b], Wybrane zastosowania uogólnionej głębi Tukeya w odpornej analizie ekonomicznej, Konferencja Statystyka Matematyczna, Wisła.
  • Kosiorowski D. [2010c], Wybrane zastosowania głębi Studenta w odpornej analizie ekonomicznej, Folia Oeconomica Cracoviensia, Posiedzenie PAN w Krakowie, 17.12.2010 r.
  • Liu R.Y., Parelius J.M., Singh K. [1999], Multivariate Analysis by Data Depth: Descriptive Statistics, Graphics and Inference (with discussion), The Annals of Statistics (27).
  • Lopez-Pintado S., Romo J. [2006], Depth-based Classification for Functional Data, red. R.Y. Liu, R., Serfling D.L. Souvaine, Series in Discrete Mathematics and Theoretical Computer Science, nr 72.
  • Lopez-Pintado S., Romo J. [2009], On the Concept of Depth for Functional Data, „Journal of the American Statistical Association”, nr 104(486).
  • Maronna R.A., Martin R.D., Yohai V.J. [2006], Robust Statistics – Theory and Methods, John Wiley & Sons Ltd, Chichester.
  • Mizera I. [2002], On Depth and Depth Poins: A Calculus, The Annals of Statistics, nr 30.
  • Mizera I., Muller C.H. [2004], Location – Scale Depth (with Discussion and Rejoinder), „Journal of the American Statistical Association”, nr 99(4).
  • Rousseeuw J.P., Hubert M. [1998], Regression Depth, „Journal of The American Statistical Association”, nr (94).
  • Tsay R.S. [2010], Analysis of Financial Time Series, Wiley – Interscience, Hoboken, New Yersey.
  • Tukey J. [1975], Mathematics and Picturing Data, red. R. James, Proceedings of the 1974 International Congress of Mathematicians, 2, Canadian Math. Congress.
  • Zuo Y., Serfling R. [2000a], General Notions of Statistical Depth Function, The Annals of Statistics, nr 28.
  • Zuo Y., Serfling R. [2000b], Structural Properties and Convergence Results for Contours of Sample Statistical Depth Functions, The Annals of Statistics, nr 28.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-db1812d2-4fe0-463d-8124-997f087b849f
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