Abstract
We consider the problem of testing the null hypothesis of no change against the alternative of exactly one change point when the change is expressed in terms of the value of the coefficient of variation. We propose a number of nonparametric test statistics for this problem. The asymptotic theory of the proposed tests is developed.
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References
E.-E. Aly, “Change Point Detection Based on L-Statistics”, Fields Inst. Comm. 44, 293–300 (2004).
G. K. Bhattacharyya, “Tests for Randomness against Trend or Serial Correlations”, in Handbook of Statistics, Ed. by P. R. Krishnaiah and P. K. Sen, Vol. 4: Nonparametric Methods (North-Holland, Amsterdam, 1984), pp. 89–111.
M. Csörgő and L. Horváth, “Nonparametric Methods for Change-Point Problems”, in Handbook of Statistics, Ed. by P. R. Krishnaiah and P. K. Sen, Vol. 7, Quality Control and Reliability (North-Holland, Amsterdam, 1988), pp. 403–425.
M. Csörgő and L. Horváth, “Invariance Principles for Change-Point Problems”, J. Multivar. Anal. 27, 151–168 (1988).
M. Csörgő and L. Horváth, Limit Theorems in Change Point Analysis (Wiley, New York, 1997).
U. Einmahl, “Strong Invariance Principles for Partial Sums of Independent Random Vectors”, Ann. Probab. 15, 1419–1440 (1987).
U. Einmahl, “Extension of Results of Komlós, Major and Tusnády to the Multivariate Case”, J. Multivar. Anal. 28, 20–68 (1989).
E. Gombay, L. Horváth, and M. Husková, “Estimators and Tests for Change in Variances”, Statist. and Dec. 14, 145–159 (1996).
M. Hušková and P. K. Sen, “Nonparametric Tests for Shift and Change in Regression at an Unknown Time Point”, in: Statistical Analysis and Forecasting of Economic Structural Change, Ed. by P. Hackl (Springer, New York, 1989), pp. 71–85.
F. Lombard, “Some Recent Developments in the Analysis of Change-Point Data”, South African Statist. J. 23, 1–21 (1989).
P. K. Sen, (1988). “Robust Tests for Change-Point Models”, in: Encyclopedia of Statistical Sciences, Ed. by S. Kotz and N. L. Johnson (Wiley, New York, 1988), Vol. 8, pp. 173–176.
G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics (Wiley, New York, 1986).
S. Zacks, “Survey of Classical and Bayesian Approaches to the Change-Point Problem: Fixed Sample and Sequential Procedures of Testing and Estimation”, in: Recent Advances in Statistics, Ed. by M. H. Rizvi, J. S. Rustagi, and D. Siegmund (Academic Press, New York, 1983), pp. 245–269.
A. Yu. Zaitsev, “Multidimensional Version of the Results of Komlós, Major and Tusnády for Vectors with Finite Exponential Moments”, ESAIM, Probab. Statist. 2, 41–108 (1998).
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Aly, E.E. Nonparametric tests for a change in the coefficient of variation. Math. Meth. Stat. 16, 369–375 (2007). https://doi.org/10.3103/S1066530707040059
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DOI: https://doi.org/10.3103/S1066530707040059