Detection of Heterogeneity in Three-Dimensional Data Sequences: Algorithm and Applications
Keywords:
Change-point problem, Rank score test, Threshold copula, Cut-point selection methodAbstract
We present a nonparametric algorithm which allows reducing the investigations of changes of the joint distribution of chronologically ordered multidimensional random sequence to the investigations of some one-dimensional conditional distributions. The algorithm is implemented with the statistical software package R. The action of the program is demonstrated on applications. The first one concerns the retrospective analysis of the changes in the concentration of chemical components of ground water preceding major seismic events. The second refers to the definition of cut-points in two-dimensional life time data sets of the imatinib-treated chronic myeloid leukemia patients.
References
R. V. Nelsen, An Introduction to Copulas, Springer, New York, 2006.
D. D. Mari, S. Kotz, Correlation and Dependence, London Imperial College Press. 2004.
A. A. Borovkov, Mathematical Statistics, (in Russian), M., "Nauka", 2007.
B. E. Brodsky, B.S. Darkhovsky, Nonparametric Methods in Change-Point Problems. Kluver, Dordrecht, 1993.
I. A. Safaryan, Nonparametric algorithms for monitoring of time series, PhD Thesis (in Russian), Yerevan, 1998.
U. N. Blagoveschensky, “The main elements of the theory of copulas", (in Russian), Applied Econometrics, N2, pp. 113-131, 2012.
A. Dias and P. Embrechts, “Change-point analysis in finance and insurance", In New Risk Mesures in Investment and Regulation, Willey, New York,pp. 2003.
B. E. Brodsky, G.I. Penikas and I.A. Safaryan, “Detecting structural changes in the copula models", (in Russian), Applied Econometrics, 4(16), pp. 3-16, 2009.
E. A. Haroutunian, I.A. Safaryan, H .M. Petrosyan and A. R. Gevorkian, “On identification of anomalies in multidimensional hydrogeochemical data as earthquake precursors", Mathematical Problems of Computer Science, vol. 40, p. 76, 2013.
U. N. Blagoveschensky, Secrets of the correlations, (in Russian), M., "Nauchnaya kniga", 2008.
E. A. Haroutunian and I. A. Safaryan, “Copulas of two-dimensional threshold models", Mathematical Problems of Computer Science, vol. 31, pp. 40-48, 2008.
U.I. Staheev, “Geochemical precursors of earthquakes", (in Russian), Russian Chemical Journal, vol. XLIX, no. 4, pp. 110-119, 2005.
E. A. Haroutunian and I. A. Safaryan, “On estimation of threshold parameter in three-dimensional copulas model", Abstracts of International Conference on Computer Science and Information Technologies, Yerevan, pp. 129-131. 2011.
B. Lausen and M. Schumacher, “Maximally selected rank statistics". Biometrics, vol. 48, pp. 73-85, 1992.
E. A. Haroutunian and I.A. Safaryan, “Nonparametric consistent estimation of random sequence change moment", (in Russian), Mathematical Problems of Computer Science, vol. 17, pp. 76-85, 1997.
H. M. Petrosyan, Precursors and Prognosis of Earthquakes on the Territory of the Republic of Armenia, (in Russian), Yerevan, 2009
J. Paik and Zh. Ying, “A composite likelihood approach for spatially correlated survival data", Computational Statistics and Data Analysis, vol. 5 6, pp. 209-216, 2012.
P. F. Su and Ch.-I. Li, Yu. Shyr, “Sample size determination for paired right-censored data based on the difference of Kaplan-Meier estimates", Computational Statistics and Data Analysis, vol. 74, pp. 39-51, 2014.
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