Optimal sampling for density estimation in continuous time

Journal of Time Series Analysis

Volumn 24, Issue 1, 2003, Pages 1-23

  Blanke, D ^a,b   Pumo, B ^a,c  

^a SORBONNE UNIVERSITÉ   (France)

^b National Institute of Horticulture ^*  (France)

^c National Institute of Horticulture   (France)

Author keywords

Density estimation; Sampling; errors in variables; Simulation; Small noise

Indexed keywords

EID: 0141873002     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9892.00290     Document Type: Article

References (29)

1. BLANKE, D. (1996) Estimation de la densité pour des trajectoires non directement observables. Publ. Inst. Stat. Univ. Paris XXXX(2), 21-36.
2. _ (2002) Estimation of local smoothness coefficients for continuous time processes. Stat. Inference Stoch. Process. 5(1), 65-93.
3. _ and BOSQ, D. (1997) Accurate rates of density estimators for continuous time processes. Statist. Probab. Lett. 33(2), 185-91.
4. _ and _ (2000) A family of minimax rates for density estimators in continuous time. Stochastic Anal. Appl. 18(6), 871-900.
5. _ and MERLEVÈDE, F. (2000) Estimation of the asymptotic variance of local time density estimators for continuous time processes. Math. Methods Statist. 9(3), 270-96.
6. BOSQ, D. (1997) Parametric rates of nonparametric estimators and predictors for continuous time processes. Ann. Statist. 25(3), 982-1000.
7. _ (1998) Nonparametric Statistics for Stochastic Processes. Estimation and Prediction, Lecture Notes in Statistics 110, 2nd ed. New-York: Springer-Verlag.
8. _ and CHEZE-PAYAUD, N. (1999) Optimal asymptotic quadratic error of nonparametric regression function estimates for a continuous-time process from sampled-data. Statistics 32(3), 229-47.
9. EFROMOVICH, S. (1999) Nonparametric curve estimation. Methods, Theory, and Applications, Springer Series in Statistics, New York: Springer-Verlag.
10. FAN, J. (1991) On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Statist. 19(2), 1257-72.
11. _ (1992) Deconvolution with supersmooth distributions. Canad. J. Stat. 20(2), 155-69.
12. GUILLOU, A. and MERLEVÈDE F. (2001) Estimation of the asymptotic variance of kernel density estimators for continuous time processes. J. Multivariate Anal. 79(1), 114-37.
13. HALL, P., LAHIRI, S. N. and TRUONG, Y. K. (1995) On bandwidth choice for density estimation with dependent data. Ann. Statist. 23, 2241-63.
14. HART, J. D. and VIEU, P. (1990) Data-driven bandwidth choice for density estimation based on dependent data. Ann. Statist. 18, 873-90.
15. KIM, T. Y. (1997) Asymptotically optimal bandwidth selection rules for the kernel density estimator with dependent observations. J. Statist. Plann. Inference 59(2), 321-36.
16. KLOEDEN, P. and PLATEN, E. (1992) Numerical Solution of Stochastic Differential Equations, Applications of Mathematics, 23, Berlin: Springer-Verlag.
17. LEBLANC, F. (1995) Discretized wavelet density estimators for continuous time stochastic processes. Wavelets and Statistics (Villard de Lans, 1994), 209-24, Lecture Notes in Statist. 103, New York: Springer.
18. LEBLANC, F. (1995) Discretized wavelet density estimators for continuous time stochastic processes. Wavelets and Statistics (Villard de Lans, 1994), 209-24, Lecture Notes in Statist. 103, New York: Springer.
19. _ (1997) Density estimation for a class of continuous time processes. Math. Methods Statist. 6(2), 171-99.
20. MASRY, E. (1983) Probability density estimation from sampled data. IEEE Trans. Inform. Theory 29, 696-709.
21. _ (1991) Multivariate probability density deconvolution for stationary processes. IEEE Trans. Inform. Theory 37, 1105-15.
22. _ (1993) Strong consistency and rates for deconvolution estimators of multivariate densities of stationary processes. Stochastic Process. Appl. 47, 53-74.
23. PRAKASA RAO, B. L. S. (1990) Nonparametric density estimation for stochastic process from sampled data. Publ. Inst. Stat. Univ. Paris XXXV, 51-84.
24. SKÖLD, M. (2001a) A bias correction for cross-validation bandwidth selection when a kernel estimate is based on dependent data. J. Time Ser. Anal. 22(4), 493-503.
25. _ (2001b) The asymptotic variance of the continuous-time kernel estimator with applications to bandwidth selection. Stat. Inference Stoch. Process. 4(1), 99-117.
26. _ and HÖSSJER, O. (1999) On the asymptotic variance of the continuous-time kernel density estimator. Statist. Probab. Lett. 44(1), 97-106.
27. STEFANSKI, L. and CARROLL, R. J. (1990) Deconvoluting kernel density estimators. Statistics 21(2), 169-84.
28. WHEEDEN, R. L. and ZYGMUND, A. (1977) Measure and Integral: An Introduction to Real Analysis. New York: M. Dekker.
29. WONG, E. (1966) Some results concerning the zero-crossings of Gaussian noise. SIAM J. Appl. Math. 14(6), 1246-54.