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http://dx.doi.org/10.5351/CKSS.2007.14.2.443

A Nonparametric Bootstrap Test and Estimation for Change  

Kim, Jae-Hee (Department of Statistics, Duksung Women's University)
Publication Information
Communications for Statistical Applications and Methods / v.14, no.2, 2007 , pp. 443-457 More about this Journal
Abstract
This paper deals with the problem of testing the existence of change in mean and estimating the change-point using nonparametric bootstrap technique. A test statistic using Gombay and Horvath (1990)'s functional form is applied to derive a test statistic and nonparametric change-point estimator with bootstrapping idea. Achieved significance level of the test is calculated for the proposed test to show the evidence against the null hypothesis. MSE and percentiles of the bootstrap change-point estimators are given to show the distribution of the proposed estimator in simulation.
Keywords
Achieved significance level; change-point; nonparametric bootstrap test; Ornstein- Uhlenbeck process;
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  • Reference
1 Boukai, B.(1993). A nonparametric bootstrapped estimate of the change-point. Journal of Nonparametric Statistics, 3, 123-134   DOI
2 Darkhovsh, B. S. (1976). A non-parametric method for the a posteriori detection of the 'disorder' time of a sequence of independent random variables. Theory of Probability and Appl., 21, 178-183   DOI
3 Page, E. S. (1955). A test for a change in a parameter occurring at an unknown point. Biometrika, 42, 523-527   DOI
4 Kander, Z. and Zacks, S. (1966). Test procedures for possible changes in parameters of statistical distributions occurring at unknown time points. The Annanls of Mathematical Statisitcs, 37, 1196-1210   DOI
5 Lorden, G. (1971). Procedures for reacting to a change in distribution. The Annanls of Mathematical Statisitcs, 42, 1897-1908   DOI
6 Pettitt, A. N. (1979). A non-parametric approach to the change-point problem. Applied Statistics, 28, 126-135   DOI   ScienceOn
7 Romano, J. P. (1989). Bootstrap and randomization tests of some nonparametric hypotheses. The Annals of Statistics, 17, 141-159   DOI
8 Zacks, S. (1983). Survey of classical and Bayesian approaches to the change-point problem: fixed sample and sequential procedures of testing and estimation. Recent Advances in Statistics, Academic Press, 245-269
9 Bhattacharyya, G. K. and Johnson, R. A. (1968). Nonparametric tests for shift at an unknown time point, Annals of Mathematical Statistics, 39, 1731-1743   DOI
10 Antoch, J. and Huskova, M. (1995). Change-point problem and bootstrap. Journal of Nonparametric Statistics, 5, 123-144   DOI
11 Carlstein, E. (1988). Nonparametric change-point estimation. The Annals of Statistics, 16, 188-197   DOI
12 Chernoff, H. and Zacks, S. (1964). Estimating the current mean of a normal distribution which is subjected to changes in time. The Annals of Mathematical Statistics, 35, 999-1018   DOI
13 Eastwood, V. R. (1993). Some nonparametric methods for changepoint problems. The Canadian Journal of Statistics, 21, 209-222   DOI   ScienceOn
14 Gombay, E. and Horvath, L. (1990b). Asymptotic distributions of maximum likelihood tests for change in the mean. Biometrika, 77, 411-414   DOI   ScienceOn
15 Efron, B, and Tibshirani, R. J. (1979). An Introduction to the Bootstrap. Chapman & Hall/CRC, London
16 Gardner, L. A. Jr.(1969). On detecting changes in the mean of normal variates. Annals of Mathematical Statistics, 40, 116-126   DOI
17 Gombay, E. and Horvath, L. (1990a). On the rate of approximations for maximum likelihood tests in change-point models. Journal of Multivariate Analysis, 56, 120-152
18 Hinkley, D. V. (1970). Inference about the change-point in a sequence of random variables. Biometrika, 57 1-17
19 Hinkley, D. and Schechtman, E. (1987). Conditional bootstrap methods in the mean-shift model. Biometrika, 74, 85-93   DOI   ScienceOn