Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
55--79
Opis fizyczny
Bibliogr. 29 poz., rys.
Twórcy
autor
- Department of Statistics, Cracow University of Economics, ul. Rakowicka 27, 31-510 Cracow, Poland
Bibliografia
- [1] Data Streams. Models and Algorithms, C.C. Aggerwal (Ed.), Springer, New York 2007.
- [2] 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.
- [3] DONOHO D., High-dimensional data analysis: The curses and blessings of dimensionality, Manuscript, 2000, http://www-stat.stanford.edu/~donoho/Lectures/AMS2000/Curses.pdf
- [4] FAN J., YAO Q., Nonlinear Time Series: Nonparametric and Parametric Methods, Springer, New York 2005.
- [5] 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.
- [6] GIJBELS I., Recent advances in estimation of conditional distributions, densities and quantiles. Keynote lecture, ERCIM 2014, Pisa.
- [7] HALL P., RODNEY C.L., YAO Q., Methods for estimating a conditional distribution function, Journal of the American Statistical Association, 1999, 94, 154–163.
- [8] 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.
- [9] HART J., Nonparametric Smoothing and Lack-of-Fit Tests, Springer, New York 1997.
- [10] HUBER P., Data Analysis: What Can Be Learned from the Past 50 Years?, Wiley, 2011.
- [11] HYNDMAN J.R., YAO R.J., Nonparametric estimation and symmetry tests for conditional density functions, Journal of Nonparametric Statistics, 2002, 14 (3), 259–278.
- [12] HYNDMAN J.R., EINBECK J., WAND M., hdrcde R package. Highest density regions and conditional density estimation, http://www.robjhyndman.com/software/hdrcde
- [13] 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.
- [14] KOSIOROWSKI D., ZAWADZKI Z., DepthProc, an R Package for Robust Exploration of Multidimensional Economic Phenomena, arXiv preprint, arXiv:1408.4542,2014.
- [15] KOSIOROWSKI D., Location – scale depth in streaming data analysis, Przegląd Statystyczny, 2012, 59, Special Issue (1), 87–108 (in Polish).
- [16] KOSIOROWSKI D., Statistical depth functions in robust economic analysis, Zeszyty Naukowe, Uniwersytet Ekonomiczny w Krakowie. Seria Specjalna, Monografie, 208, 2012 (in Polish).
- [17] 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/
- [18] LI J., LIU R.Y., New nonparametric tests of multivariate locations and scales using data depth, Statistical Science, 2004, 19, 686–696.
- [19] MARONNA R.A., MARTIN R.D., YOHAI V.J., Robust Statistics. Theory and Methods, Wiley, Chichester 2006.
- [20] MUTHUKRISHAN S., Data Streams. Algorithms and Applications, Now Publishers, Boston 2006.
- [21] PAINDAVEINE D., VAN BEVER G., From depth to local depth. A focus on centrality, Journal of the American Statistical Association, 2013, 105, 1105–1119.
- [22] RACINE J.S., Nonparametric econometrics. A Primer, Foundations and Trends in Econometrics, 2008, 1 3 (1), 1–88.
- [23] STOCKIS J.-P., FRANKE J., KAMGAING J.T., On geometric ergodicity of CHARME models, Journal of the Time Series Analysis, 2010, 31, 141–152.
- [24] TSAY R., Analysis of Financial Time Series, Wiley, New York 2010.
- [25] TSYBAKOV A.B., Introduction to Nonparametric Estimation, Springer, New York 2010.
- [26] WAND M.P., JONES M.C., Kernel Smoothing, Monographs on Statistics and Applied Probability, 60, Chapman and Hall, London 1994.
- [27] ZUO Y., Projection-based depth functions and associated medians, Annals of Statistics, 2004, 31, 1460–1490.
- [28] ZUO Y., Robustness of weighted lp depth and lp median, Allgemaines Statistisches Archiv, 2004, 88, 215–234.
- [29] 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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-571e7de6-f7d0-4465-8ede-a6abc0107a58