Browse > Article
http://dx.doi.org/10.5351/CKSS.2009.16.4.587

Test for Distribution Change of Dependent Errors  

Na, Seong-Ryong (Department of Information and Statistics, Yonsei University)
Publication Information
Communications for Statistical Applications and Methods / v.16, no.4, 2009 , pp. 587-594 More about this Journal
Abstract
In this paper the change point problem of the error terms in linear regression models is considered. Since fixed or stochastic independent variables and weakly dependent errors are assumed, usual multiple regression models and time series models including ARMA are covered. We use the estimates of probability density function based on residuals in order to test the distribution change of the unobserved errors. Under some mild conditions, the test using the residuals is proved to have the same limiting distribution as the test based on true errors.
Keywords
Change point; time series; dependent error; strong mixing; estimation of probability density function;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Chanda, K. C. (1995). Large sample analysis of autoregressive moving-average models with errors in variables, Journal of Time Series Analysis, 16, 1-15   DOI
2 Doukahn, P. (1994), Mixing: Properties and Examples, Springer, New York
3 Lee, S. and Na, S. (2002). On the Bickel-Rosenblatt test for first-order autoregressive models, Statistics and Probability Letters, 56, 23-35   DOI   ScienceOn
4 Lee, S. and Na, S. (2004). A nonparametric test for the change of the density function in strong mixing processes, Statistics and Probability Letters, 66, 25-34   DOI   ScienceOn
5 Ling, S. (1998). Weak convergence of the sequential empirical processes of residuals in nonstationary autoregressive models, Annals of Statistics, 26, 741-754   DOI   ScienceOn
6 Na, S., Lee, S. and Park, H. (2006). Sequential empirical process in autoregressive models with measure-ment errors, Journal of Statistical Planning and Inference, 136, 4204-4216   DOI   ScienceOn
7 Silverman, B. W. (1986). Density estimation for statistics and data analysis, Chapman and Hall, London
8 Takahata, H. and Yoshihara, K. (1987). Central limit theorems for integrated square error of nonparametric density estimators based on absolutely regular random sequences, Yokohama Mathematics Journal, 35, 95-111
9 Billingsley, P. (1999). Convergence of Probability Measures, 2nd edition, John Wiley & Sons, New York
10 Bai, J. (1994). Weak convergence of the sequential empirical processes of residuals in ARMA models, Annals of Statistics, 22, 2051-2061   DOI   ScienceOn
11 Bosq, D. (1998). Nonparametric Statistics for Stochastic Processes, 2nd edition, Springer, New York