On multivariate quantile regression

Journal of Statistical Planning and Inference

Volumn 110, Issue 1-2, 2003, Pages 109-132

  Chakraborty, Biman ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Data driven coordinates; Equivariance; Multiresponse linear models; Transformation retransformation

Indexed keywords

EID: 33846379527     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(01)00277-4     Document Type: Article

References (37)

1. Babu, G.J., 1989. Strong representations for lad estimators in linear models. Probab. Theory Related Fields 83, 547-558.
2. Bai, Z.D., Chen, N.R., Miao, B.Q., Rao, C.R., 1990. Asymptotic theory of least distances estimate in multivariate linear models. Statistics 21, 503-519.
3. Bickel, P.J., 1964. On some alternative estimates for shift in the p-variate one sample problem. Ann. Math. Statist. 35, 1079-1090.
4. Bickel, P.J., 1973. On some analogues of linear combinations of order statistics in linear model. Ann. Statist. 1, 597-616.
5. Bloomfield, P., Steiger, W.L., 1983. Least Absolute Deviations Theory, Applications and Algorithms. Birkhauser, Boston.
6. Brown, B.M., 1983. Statistical use of spatial median. J. Roy. Statist. Soc. Ser. B 45, 25-30.
7. Brown, B.M., 1985. Spatial median, In: Encyclopedia of Statistical Science, Vol. 8, Wiley, New York, pp. 574-575.
8. Brown, B.M., Hettmansperger, T.P., 1987. A4ne invariant rank methods in bivariate location model. J. Roy. Statist. Soc. Ser. B 49, 301-310.
9. Brown, B.M., Hettmansperger, T.P., 1989. An a4ne invariant bivariate version of the sign test. J. Roy. Statist. Soc. Ser. B 51, 117-125.
10. Chakraborty, B., 1999. On multivariate median regression. Bernoulli 5, 683-703.
11. Chakraborty, B., 2001. On a4ne equivariant multivariate quantiles. Ann. Inst. Statist. Math. 53, 380-403.
12. 1-Statistical Procedures and Related Topics, IMS Lecture Notes-Monograph Series, Vol. 31, pp. 399-414.
13. Chakraborty, B., Chaudhuri, P., Oja, H., 1998. Operating transformation retransformation on spatial median and angle test. Statist. Sinica 8, 767-784.
14. Chaudhuri, P., 1991a. Nonparametric estimates of regression quantiles and their local Bahadur representation. Ann. Statist. 19, 760-777.
15. Chaudhuri, P., 1991b. Global nonparametric estimation of conditional quantile functions and their derivatives. J. Multivariate Anal. 39, 246-269.
16. 1 Statistical Analysis and Related Methods. North-Holland, Amsterdam, pp. 169-185.
17. Chaudhuri, P., 1996. On a geometric notion of quantiles for multivariate data. J. Amer. Statist. Assoc. 91, 862-872.
18. Chaudhuri, P., Sengupta, D., 1993. Sign tests in multidimension: inference based on the geometry of the data cloud. J. Amer. Statist. Assoc. 88, 1363-1370.
19. Cole, T.J., 1988. Fitting smoothed centile curves to reference data. J. Roy. Statist. Soc. Ser. A 151, 385-418.
20. Efron, B., 1991. Regression percentiles using asymmetric squared error loss. Statist. Sinica 1, 93-125.
21. Huber, P., 1973. Robust regression, asymptotics, conjectures and Monte-Carlo. Ann. Statist. 1, 799-821.
22. Johnson, R.A., Wichern, D.W., 1998. Applied Multivariate Statistical Analysis. Prentice-Hall, Englewood CliOs, NJ.
23. Jureckova, J., Sen, P.K., 1996. Robust Statistical Procedures: Asymptotics and Interrelations. Wiley, New York.
24. 1-norm and Related Methods. North-Holland, Amsterdam, pp. 217-230.
25. Koenker, R., Bassett, G., 1978. Regression quantiles. Econometrica 46, 33-50.
26. Koenker, R., d'Orey, V., 1987. Algorithm AS 229: computing regression quantiles. Appl. Statist. 36, 383-393.
27. Koenker, R., Portnoy, S., 1987. L estimation for linear models. J. Amer. Statist. Assoc. 82, 851-857.
28. Koenker, R., Portnoy, S., 1990. M estimation of multivariate regressions. J. Amer. Statist. Assoc. 85, 1060-1068.
29. Koltchinskii, V., 1997. M-estimation, convexity and quantiles. Ann. Statist. 25, 435-477.
30. Krishnakumar, J., Ronchetti, E., 1997. Robust estimators for simultaneous equations models. J. Econometrics 78, 295-314.
31. Maronna, R.A., Yohai, V.J., 1997. Robust estimation in simultaneous equations models. J. Statist. Plann. Inference 57, 233-244.
32. Narula, S.C., Wellington, J.F., 1977. Algorithm AS 108: multiple linear regression with minimum sum of absolute errors. Appl. Statist. 26, 106-111.
33. Niemiro, W., 1992. Asymptotics for M-estimators de8ned by convex minimization. Ann. Statist. 20, 1514-1533.
34. 1-norm in statistical inference. SankhyaT, Ser. A 50, 289-313.
35. Ruppert, D., Carroll, R.J., 1980. Trimmed least squares estimation in the linear model. J. Amer. Statist. Assoc. 75, 828-838.
36. Welsh, A.H., 1987a. The trimmed mean in the linear model (with comments). Ann. Statist. 15, 20-45.
37. Welsh, A.H., 1987b. One-step L estimation in linear model. Ann. Statist. 15, 626-641.