Pointwise convergence rates and central limit theorems for kernel density estimators in linear processes

Statistics and Probability Letters

Volumn 76, Issue 16, 2006, Pages 1756-1760

  Schick, Anton ^a   Wefelmeyer, Wolfgang ^b  

^a BINGHAMTON UNIVERSITY   (United States)

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Lipschitz continuity; Martingale approximation; Smoothness of convolutions

Indexed keywords

EID: 33747160416     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2006.04.021     Document Type: Article

References (9)

1. Bryk A., and Mielniczuk J. Asymptotic properties of density estimates for linear processes: application of projection method. J. Nonparametr. Stat. 17 (2005) 121-133
2. Hall P., and Hart J.D. Convergence rates in density estimation for data from infinite-order moving average processes. Probab. Theory Related Fields 87 (1990) 253-274
3. Hallin M., and Tran L.T. Kernel density estimation for linear processes: asymptotic normality and optimal bandwidth derivation. Ann. Inst. Stat. Math. 48 (1996) 429-449
4. Lu Z. Asymptotic normality of kernel density estimators under dependence. Ann. Inst. Stat. Math. 53 (2001) 447-468
5. Parzen E. On estimation of a probability density function and mode. Ann. Math. Stat. 33 (1962) 1065-1076
6. Rudin W. Real and Complex Analysis. second ed (1974), McGraw-Hill, New York
7. 1-norms. J. Stat. Plan. Infer., to appear.
8. Tran L.T. Kernel density estimation for linear processes. Stochastic Process. Appl. 41 (1992) 281-296
9. Wu W.B., and Mielniczuk J. Kernel density estimation for linear processes. Ann. Stat. 30 (2002) 1441-1459