References
- Azzalini , A. 1981 . A note on the estimation of a distribution function and quantiles by a kernel method . Biometrika , 68 : 326 – 328 .
- Barlow , R. E. and Proschan , F. 1975 . Statistical Theory of Reliability and Life Testing: Probability Models , New York : Holt, Rinehart and Winston .
- Birkel , T. 1988a . Moment bounds for associated sequences . Ann. Probab. , 16 : 1184 – 1193 .
- Birkel , T. 1988b . On the convergence rate in the central limit theorem for associated processes . Ann. Probab. , 16 : 1685 – 1698 .
- Brindley , E. C. Jr. and Thompson , W. A. Jr. 1972 . Dependence and aging aspects of multivariate survival . J. Amer. Statist. Assoc. , 67 : 822 – 830 .
- Cai , Z. 1993 . Uniform strong convergence and rates for the kernel estimators of a distribution function and a regression function under weakly dependent assumptions . Chinese J. Applied Probab. Statist. , 9 : 11 – 17 .
- Cai , Z. and Roussas , G. G. 1992 . Uniform strong estimation under α-mixing, with rates . Statist. Probab. Lett. , 15 : 47 – 55 .
- Cai Z. Roussas G. G. Berry-Esseen bounds for smooth estimator of a distribution function under association Technical Report No. 306 Division of Statistics, University of California-Davis 1995
- Cai , Z. and Roussas , G. G. 1997a . Efficient estimation of a distribution function under quadrant dependence . Scand. J. Statist. , 25 : 211 – 224 .
- Cai , Z. and Roussas , G. G. 1997b . Smooth estimator of quantiles under association . Statist. Probab. Letters , To appear
- Esary , J. D. , Proschan , F. and Walkup , D. W. 1967 . Association of random variables, with applications . Ann. Math. Statist. , 38 : 1466 – 1474 .
- Falk , M. 1983 . Relative efficiency and deficiency of kernel type estimators of smooth distribution functions . Statist. Neerlandica , 37 : 73 – 83 .
- Fortuin , C. M. , Kastelyn , P. W. and Ginibre , J. 1971 . Correlation inequalities on some partially ordered sets . Commun. Math. Phys. , 22 : 89 – 103 .
- Hall , P. 1982 . Rates of Convergence in the Central Limit Theorem , London : Pitman .
- Harris , T. E. 1960 . A lower bound for the critical probability in a certain percolation process . Proc. Camb. Phil. Soc. , 56 : 13 – 20 .
- Joag-Dev , K. 1983 . Independence via uncorrelatedness under certain dependence structures . Ann. Probab. , 11 : 1037 – 1041 .
- Joag-Dev , K. and Proschan , F. 1983 . Negative association of random variables, with applications . Ann. Statist. , 11 : 286 – 295 .
- Lehmann , E. 1966 . Some concepts of dependence . Ann. Math. Statist. , 37 : 1137 – 1153 .
- Lejeune , M. and Sarda , P. 1992 . Smooth estimators of distribution and density functions . Comput. Statist. Data Anal. , 14 : 457 – 471 .
- Nadaraya , E. A. 1964 . Some new estimates for distribution function . Theory Probab. Appl. , 9 : 497 – 500 .
- Newman , C. M. 1980 . Normal fluctuations and the FKG inequalities . Commun. Math. Phys. , 74 : 119 – 128 .
- Newman C. M. Asymptotic independence and limit theorems for positively and negatively dependent random variables Inequality in Statistics and Probability Tong Y. L. IMS Lecture Notes-Monograph Series 1984 5 127 140
- Newman C. M. Ising models and dependent percolation Topics in Statistical Dependence Block H. W. Sampson A. R. Savits T. H. IMS Lecture Notes-Monograph Series 1990 16 395 401
- Reiss , R. D. 1981 . Nonparametric estimation of smooth distribution functions . Scand. J. Statist. , 8 : 116 – 119 .
- Roussas , G. G. 1969 . Nonparametric estimation of the transition distribution function of a Markov process . Ann. Math. Statist. , 40 : 1386 – 1400 .
- Roussas G. G. Smooth estimation of the distribution function under association: Asymptotic normality Technical Report No. 289 Division of Statistics, University of California Davis 1993
- Roussas , G. G. 1995 . Asymptotic normality of a smooth estimate of a random field distribution function under association . Statist. Probab. Lett. , 24 : 77 – 90 .
- Sadikova , S. M. 1966 . Two dimensional analogues of an inequality of Esseen with applications to the central limit theorem . Theory Probab. Appl. , 11 : 325 – 335 .
- Sarda , P. 1993 . Smoothing parameter selection for smooth distribution functions . J. Statist. Plann. Inference , 35 : 65 – 75 .
- Shaked , M. 1982 . A general theory of some positive dependence notions . J. Multivariate Anal. , 12 : 199 – 218 .
- Shao , Q. M. 1986 . A Berry-Esseen inequality and an invariance principle for associated random fields . Chinese J. Applied Probab. Statist. , 5 : 1 – 8 .
- Stout , W. F. 1974 . Almost Sure Convergence , New York : Academic Press .
- Tikhomirov , A. N. 1980 . On the convergence rate in the central limit theorem for weakly dependent random variables . Theory Probab. Appl. , 25 : 790 – 809 .
- Watson , G. S. and Leadbetter , M. R. 1964 . Hazard analysis II . Sankhyā Ser. A , 26 : 101 – 116 .
- Winter , B. B. 1973 . Strong uniform consistency of integrals of density estimators . Canad. J. Statist. , 1 : 247 – 253 .
- Winter , B. B. 1979 . Convergence rate of perturbed empirical distribution functions . J. Appl. Probab. , 16 : 163 – 173 .
- Wood , T. 1983 . A Berry-Esseen theorem for associated random variables . Ann. Probab. , 4 : 1042 – 1047 .
- Yamato , H. 1973 . Uniform convergence of an estimator of a distribution function . Bull. Math. Statist. , 15 : 69 – 78 .