Effect of dependence on stochastic measures of accuracy of density estimators

Annals of Statistics

Volumn 30, Issue 2, 2002, Pages 431-454

  Claeskens, Gerda ^a   Hall, Peter ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Bandwidth; Cross validation; Gaussian process; Integrated squared error; Kernel methods; Long range dependence; Nonparametric density estimator; Risk based analysis

Indexed keywords

EID: 0036281479     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1021379860     Document Type: Article

References (28)

1. AHMAD, I. A. (1982). Integrated mean square properties of density estimation by orthogonal series methods for dependent variables. Ann. Inst. Statist. Math. 34 339-350.
2. BARNDORFF-NIELSEN, O. E. and Cox, D. R. (1989). Asymptotic Techniques for Use in Statistics. Chapman and Hall, London.
3. CASTELLANA, J. V. (1989). Integrated consistency of smoothed probability density estimators for stationary sequences. Stochastic Process. Appl. 33 335-346.
4. CASTELLANA, J. V. and LEADBETTER, M. R. (1986). On smoothed probability density estimation for stationary processes. Stochastic Process. Appl. 21 179-193.
5. CHENG, B. and ROBINSON, P. M. (1991). Density estimation in strongly dependent nonlinear time series. Statist. Sinica 1 335-359.
6. CSÖRGO, S. and MIELNICZUK, J. (1995). Density estimation under long-range dependence. Ann. Statist. 23 990-999.
7. HALL, P. (1997). Defining and measuring long-range dependence. In Nonlinear Dynamics and Time Series: Building a Bridge between the Natural and Statistical Sciences (C. D. Cutler and D. T. Kaplan, eds.) 153-160. Amer. Math. Soc., Providence, RI.
8. HALL, P. and HART, J.D. (1990). Nonparametric regression with long-range dependence. Stochastic Process. Appl. 36339-351.
9. HALL, P. and JOHNSTONE, I. (1992). Empirical functional and efficient smoothing parameter selection (with discussion). J. Roy. Statist. Soc. Ser. B 54 475-531.
10. HALL, P., LAHIRI, S. N. and TRUONG, Y. K. (1995). On bandwidth choice for density estimation with dependent data. Ann. Statist. 23 2241-2263.
11. HALL, P. and MARRON, J. S. (1987). Extent to which least-squares cross-validation minimizes integrated square error in nonparametric density estimation. Probab. Theory Related Fields 74 567-581.
12. HALL, P. and MINNOTTE, M. C. (2000). High-order data sharpening for density estimation. Manuscript.
13. HÄRDLE, W., HALL, P. and MARRON, J. S. (1988). How far are automatically chosen regression smoothing parameters from their optimum? (with discussion). J. Amer. Statist. Assoc. 83 86-101.
14. HÄRDLE, W., LÜTKEPOHL, H. and CHEN, R. (1997). A review of nonparametric time series analysis. Internat. Statist. Rev. 65 49-72.
15. HART, J. D. (1996). Some automated methods of smoothing time-dependent data. J. Nonparametr. Statist. 6115-142.
16. HART, J. D. and VIEU, P. (1990). Data-driven bandwidth choice for density estimation based on dependent data. Ann. Statist. 18 873-890.
17. KIM, T. Y. and Cox, D. D. (1997). A study of bandwidth selection in density estimation under dependence. J. Multivariate Anal. 62 190-203.
18. MASRY, E. and FAN, J. (1997). Local polynomial estimation of regression functions for mixing processes. Scand. J. Statist. 24 165-179.
19. NGUYEN, H. T. (1979). Density estimation in a continuous-time stationary Markov process. Ann. Statist. 7 341-348.
20. PRAKASA RAO, B. L. S. (1978). Density estimation for Markov processes using delta sequences. Ann. Inst. Statist. Math. 30 321-328.
21. RBINSON, P. M. (1991). Nonparametric function estimation for long memory time series. In Non-parametric and Semiparametric Methods in Econometrics and Statistics: Proceedings of the 5th International Symposium in Economic Theory and Econometrics (W. W. Barnett, J. Powell and G. E. Tauchen, eds.) 437-457. Cambridge Univ. Press.
22. ROSENBLATT, M. (1970). Density estimates and Markov sequences. In Nonparametric Techniques in Statistical Inference (M. L. Puri, ed.) 199-213. Cambridge Univ. Press.
23. ROUSSAS, G. (1969). Nonparametric estimation in Markov processes. Ann. Inst. Statist. Math. 21 73-87.
24. ROUSSAS, G. (1990). Asymptotic normality of the kernel estimate under dependence conditions: application to hazard rate. J. Statist. Plann. Inference 25 81-104.
25. ROUSSAS, G. and IOANNIDES, D. A. (1987). Note on the uniform convergence of density estimates for mixing random variables. Statist. Probab. Lett. 5 279-285.
26. TAQQU, M. S. (1975). Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. Verw. Gebiete 31 287-302.
27. 1 convergence of kernel density estimates under dependence. Canad. J. Statist. 17 197-208.
28. TRAN, L. T. (1990). Kernel density estimation under dependence. Statist. Probab. Lett. 10 193-201.