Laws of iterated logarithm and related asymptotics for estimators of conditional density and mode

Annals of the Institute of Statistical Mathematics

Volumn 52, Issue 4, 2000, Pages 630-645

  Mehra, K L ^a   Ramakrishnaiah, Y S ^b   Sashikala, P ^c  

^a UNIVERSITY OF ALBERTA   (Canada)

^b OSMANIA UNIVERSITY   (India)

^c BBCIT Kachiguda ^*  (India)

Author keywords

Conditional density; Conditional mode; Law of iterated logarithm; Smooth rank nearest neighbor estimators; Uniform strong convergence

Indexed keywords

EID: 6744257502     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017517124707     Document Type: Article

References (11)

1. Dvoretzky, A., Kiefer, J. and Wolfowitz, J. (1956). Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator, Ann. Math. Statist., 27, 642-669.
2. Hall, P. (1981). Laws of iterated logarithm for nonparametric density estimators, Z. Wahrsch. Verw. Gebiete., 56, 47-61.
3. Hardle, W., Janssen, P. and Serfling, R. (1988). Strong uniform convergence rates for estimators of conditional functions, Ann. Statist., 16, 1428-1499.
4. Horvath, L. and Yandell, B. S. (1988). Asymptotics of conditional empirical processes, J. Multivariate Anal., 26, 184-206.
5. Kiefer, J. and Walfowitz, J. (1958). On the derivations of the empiric distribution function of vector chance variables, Trans. Amer. Math. Soc., 87, 173-186.
6. Mehra, K. L. and Rama Krishnaiah, Y. S. (1997). Bahadur representation and the law of the iterated logarithm for smooth conditional quantile estimators, Tech. Report, No. 2, Department of Mathematical Sciences, University of Alberta Edmonton, Canada T6G 2G1.
7. Samanta, M. and Thavaneswaran, A. (1990). Nonparametric estimation of the conditional mode, Comm. Statist. Theory Methods, 19 (12), 4515-4524.
8. Stone, C. J. (1977). Consistent nonparametric regression, Ann. Statist., 5, 595-645.
9. Stute, W. (1982). The oscillation behavior of empirical process, Ann. Probab., 10, 86-107.
10. Stute, W. (1984). The oscillation behaviour of empirical processes: The multivariate case, Ann. Probab., 12, 361-379.
11. Stute, W. (1986). On almost sure convergence of conditional empirical distribution functions, Ann. Probab., 4, 891-901.