PL EN


2015 | 25 | 1 | 55-79
Article title

Two procedures for robust monitoring of probability distributions of economic data stream induced by depth functions

Content
Title variants
Languages of publication
EN
Abstracts
EN
Data streams (streaming data) consist of transiently observed, evolving in time, multidimensional data sequences that challenge our computational and/or inferential capabilities. We propose user friendly approaches for robust monitoring of selected properties of unconditional and conditional distributions of the stream based on depth functions. Our proposals are robust to a small fraction of outliers and/or inliers, but at the same time are sensitive to a regime change in the stream. Their implementations are available in our free R package DepthProc
Year
Volume
25
Issue
1
Pages
55-79
Physical description
Contributors
  • Department of Statistics, Cracow University of Economics, ul. Rakowicka 27, 31-510 Cracow, Poland
References
  • Data Streams. Models and Algorithms, C.C. Aggerwal (Ed.), Springer, New York 2007.
  • ANAGNOSTOPOULOS C., TASOULIS D.K., ADAMS N.M., PAVLIDIS N.G., HAND D.J., Online linear and quadratic discriminant analysis with adaptive forgetting for streaming classification, Statistical Analysis and Data Mining, 2012, 5, 139–166.
  • DONOHO D., High-dimensional data analysis: The curses and blessings of dimensionality, Manuscript, 2000, http://www-stat.stanford.edu/~donoho/Lectures/AMS2000/Curses.pdf
  • FAN J., YAO Q., Nonlinear Time Series: Nonparametric and Parametric Methods, Springer, New York 2005.
  • GENTON M.G., LUCAS A., Comprehensive definitions of breakdown points for independent and dependent observations, Journal of the Royal Statistical Society Series B, 2003, 65, 81–84.
  • GIJBELS I., Recent advances in estimation of conditional distributions, densities and quantiles. Keynote lecture, ERCIM 2014, Pisa.
  • HALL P., RODNEY C.L., YAO Q., Methods for estimating a conditional distribution function, Journal of the American Statistical Association, 1999, 94, 154–163.
  • HALL P., RACINE J., LI Q., Cross-validation and the estimation of conditional probability densities, Journal of the American Statistical Association, 2004, 99, 1015–1026.
  • HART J., Nonparametric Smoothing and Lack-of-Fit Tests, Springer, New York 1997.
  • HUBER P., Data Analysis: What Can Be Learned from the Past 50 Years?, Wiley, 2011.
  • HYNDMAN J.R., YAO R.J., Nonparametric estimation and symmetry tests for conditional density functions, Journal of Nonparametric Statistics, 2002, 14 (3), 259–278.
  • HYNDMAN J.R., EINBECK J., WAND M., hdrcde R package. Highest density regions and conditional density estimation, http://www.robjhyndman.com/software/hdrcde
  • KOSIOROWSKI D., ZAWADZKI Z., Selected issues related to online calculation of multivariate robust measures of location and scatter, Proceedings of 8th A. Zeliaś International Conference, Zakopane 2014, 87–96.
  • KOSIOROWSKI D., ZAWADZKI Z., DepthProc, an R Package for Robust Exploration of Multidimensional Economic Phenomena, arXiv preprint, arXiv:1408.4542,2014.
  • KOSIOROWSKI D., Location – scale depth in streaming data analysis, Przegląd Statystyczny, 2012, 59, Special Issue (1), 87–108 (in Polish).
  • KOSIOROWSKI D., Statistical depth functions in robust economic analysis, Zeszyty Naukowe, Uniwersytet Ekonomiczny w Krakowie. Seria Specjalna, Monografie, 208, 2012 (in Polish).
  • Robust decision procedures in economic data stream analysis, D. Kosiorowski (Ed.), Technical Report 1, Cracow University of Economics, Cracow 2014, http://www.katstat.uek.krakow.pl/pl/
  • LI J., LIU R.Y., New nonparametric tests of multivariate locations and scales using data depth, Statistical Science, 2004, 19, 686–696.
  • MARONNA R.A., MARTIN R.D., YOHAI V.J., Robust Statistics. Theory and Methods, Wiley, Chichester 2006.
  • MUTHUKRISHAN S., Data Streams. Algorithms and Applications, Now Publishers, Boston 2006.
  • PAINDAVEINE D., VAN BEVER G., From depth to local depth. A focus on centrality, Journal of the American Statistical Association, 2013, 105, 1105–1119.
  • RACINE J.S., Nonparametric econometrics. A Primer, Foundations and Trends in Econometrics, 2008, 1 3 (1), 1–88.
  • STOCKIS J.-P., FRANKE J., KAMGAING J.T., On geometric ergodicity of CHARME models, Journal of the Time Series Analysis, 2010, 31, 141–152.
  • TSAY R., Analysis of Financial Time Series, Wiley, New York 2010.
  • TSYBAKOV A.B., Introduction to Nonparametric Estimation, Springer, New York 2010.
  • WAND M.P., JONES M.C., Kernel Smoothing, Monographs on Statistics and Applied Probability, 60, Chapman and Hall, London 1994.
  • ZUO Y., Projection-based depth functions and associated medians, Annals of Statistics, 2004, 31, 1460–1490.
  • ZUO Y., Robustness of weighted lp depth and lp median, Allgemaines Statistisches Archiv, 2004, 88, 215–234.
  • ZUO Y., HE X., On the limiting distributions of multivariate depth-based rank sum statistics and related tests, The Annals of Statistics, 2006, 34, 2879–2896.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-f620a156-e527-428c-bfdc-dbf4612217a3
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