Power Comparison between Methods of Empirical Process and a Kernel Density Estimator for the Test of Distribution Change

- Journal title : Communications for Statistical Applications and Methods
- Volume 18, Issue 2, 2011, pp.245-255
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2011.18.2.245

Title & Authors

Power Comparison between Methods of Empirical Process and a Kernel Density Estimator for the Test of Distribution Change

Na, Seong-Ryong; Park, Hyeon-Ah;

Na, Seong-Ryong; Park, Hyeon-Ah;

Abstract

There are two nonparametric methods that use empirical distribution functions and probability density estimators for the test of the distribution change of data. In this paper we investigate the two methods precisely and summarize the results of previous research. We assume several probability models to make a simulation study of the change point analysis and to examine the finite sample behavior of the two methods. Empirical powers are compared to verify which is better for each model.

Keywords

Test for distribution change;empirical distribution function;probability density estimator;nonparametric test;simulation study;

Language

Korean

References

1.

나성룡(2009). 종속오차에대한분포변화검정법, <한국통계학회논문집>, 16, 587–594.

2.

Bai, J. (1994). Weak convergence of the sequential empirical processes of residuals in ARMA models, Annals of Statistics, 22, 2051–2061.

3.

Berkes, I. and Horvath, L. (2003). Limit results for the empirical process of squared residuals in GARCH models, Stochastic Processes and their Applications, 105, 271–298.

4.

Berkes, I., Hormann, S. and Schauer, J. (2009). Asymptotic results for the empirical process of stationary sequences, Stochastic Processes and their Applications, 119, 1298–1324.

5.

Bickel, P. J. and Wichura, M. J. (1971). Convergence criteria for multiparameter stochastic processes and some applications, Annals of Mathematical Statistics, 42, 1656–1670.

6.

Billingsley, P. (1999). Convergence of Probability Measures, 2nd edition, John Wiley & Sons, New York.

7.

Bosq, D. (1998). Nonparametric Statistics for Stochastic Processes, 2nd edition, Springer, New York.

8.

Horvath, L., Kokoszka, P. and Teyssiere, G. (2001). Empirical process of the squared residuals of an ARCH sequence, Annals of Statistics, 29, 445–469.

9.

Koul, H. (1996). Asymptotics of some estimators and sequential residual empiricals in nonlinear time series, Annals of Statistics, 24, 380–404.

10.

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.

11.

Ling, S. (1998). Weak convergence of the sequential empirical processes of residuals in nonstationary autoregressive models, Annals of Statistics, 26, 741–754.

12.

Na, S., Lee, S. and Park, H. (2006). Sequential empirical process in autoregressive models with measurement errors, Journal of Statistical Planning and Inference, 136, 4204–4216.

13.

Picard, D. (1985). Testing and estimating change-points in time series, Advances in Applied Probability, 17, 841–867.

14.

Shorack, G. and Wellner, J. (1986). Empirical Processes with Applications in Statistics, John Wiley & Sons, New York.

15.

Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, Chapman & Hall, London.