Law of the iterated logarithm for empirical cumulative quantile regression functions

Statistica Sinica

Volumn 6, Issue 3, 1996, Pages 693-702

  Rao, C R ^a   Zhao, L C ^a  

^a NONE

Author keywords

Cumulative quantile regression function; Lorenz curves; Quantile regression function; Relative compactness; Reproducing kernel Hilbert space; Strassen's law of the iterated logarithm

Indexed keywords

EID: 21444460821     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. Bishop, J. A., Chakraborti, S. and Thistle, P. D. (1989). Asymptotically distribution-free statistical inference for generalized Lorenz curves. Rev. Econom. Statist. 71, 725-727.
2. Gastwirth, J. L. (1971). A general definition of the Lorenz curve. Econometrika 39, 1037-1039.
3. Gastwirth, J. L. (1972). The estimation of the Lorenz curve and Gini index. Rev. Econom. Statist. 54, 306-316.
4. Goldie, C. M. (1977). Convergence theorems for empirical Lorenz curves and their inverses. Adv. in Appl. Probab. 9, 765-791.
5. James, B. R. (1975). A functional law for the iterated logarithm for weighted empirical distributions. Ann. Probab, 3, 762-772.
6. Kakwani, N. C. and Fodder, N. (1973). On the estimation of Lorenz curves from grouped observations. Internat. Econom. Rev. 14, 278-292.
7. Kakwani, N. C. and Fodder, N. (1976). Efficient estimation of the Lorenz curve and associated inequality measures from grouped observations. Econometrika 44, 137-148.
8. Kuelbs, J. (1976). A strong convergence theorem for Danach space valued random variables. Ann. Probab. 4, 744-771.
9. Ledoux, M. and Talagrand, M. (1991). Probability in Banach Space. Springer-Verlag, New York.
10. Rao, C. R. and Zhao, L. C. (1995a). Convergence theorems for empirical cumulative quantile regression function. Mathematical Methods of Statistics 4, 81-91.
11. Rao, C. R. and Zhao, L. C. (1995b). Strassen's law of iterated logarithms for Lorenz curves. J. Multivariate Anal. 54, 239-252.
12. Riesz, F. and Sz-Nagy, B. (1955). Functional Analysis. Ungar, New York.
13. Shorack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics. John Wiley, New York.