M-estimation, convexity and quantiles

Arcones, M. and Gin´e, E. (1991). Some bootstrap tests of sy mmetry for univariate distributions. Ann. Statist. 19 1496-1511.

Bai, Z. D., Rao, C. R. and Wu, Y. (1992). M-estimation of a multivariate linear regression parameters under a convex discrepancy function. Statist. Sinica 2 237-254.

Baringhaus, L. (1991). Testing for spherical sy mmetry of a multivariate distribution. Ann. Statist. 19 899-917.

Barnett, V. (1976). The ordering of multivariate data (with comments). J. Roy. Statist. Soc. Ser. A 139 318-354.

Beran, R. (1979). Testing for ellipsoidal sy mmetry of a multivariate density. Ann. Statist. 7 150- 162.

Dudley, R. M. (1984). A course on empirical processes. ´Ecole d'ete de Probabilit´es de Saint-Flour XII. Lecture Notes in Math. 1097 1-142. Springer, Berlin.

Einhmahl, J. H. J. and Mason, D. (1992). Generalized quantile process. Ann. Statist. 20 1062- 1078.

Gelfand, I. M. and Shilov, G. E. (1964). Generalized Functions 1. Properties and Operations. Academic Press, New York.

Gin´e, E. and Zinn, J. (1990). Bootstrapping general empirical measures. Ann. Probab. 18 851- 869.

Gutenbrunner, C. and Jure ckov´a, J. (1992). Regression quantile and regression rank score process in the linear model and derived statistics. Ann. Statist. 20 305-330.

Gutenbrunner, C., Jure ckov´a, J., Koenker, R. and Portnoy, S. (1993). Tests of linear hy potheses based on regression rank scores. J. Nonparametr. Statist. 2 307-331.

Haberman, S. J. (1989). Concavity and estimation. Ann. Statist. 17 1631-1661.

Haldane, J. B. S. (1948). Note on the median of a multivariate distribution. Biometrika 35 414- 415.

Huber, P. J. (1967). The behavior of maximum likelihood estimates under non-standard conditions. Proc. Fifth Berkeley Sy mp. Math. Statist. Probab. 1 221-233. Univ. California Press, Berkeley.

Ioffe, A. D. and Tihomirov, V. M. (1974). The Theory of Extremal Problems. Nauka, Moscow. (In Russian.)

Koenker, R. and Basset, G. (1978). Regression quantiles. Econometrica 46 33-50.

Koenker, R. and Portnoy, S. (1987). L-estimators for linear models. J. Amer. Statist. Assoc. 82 851-857.

Koltchinskii, V. (1996). M-estimation and spatial quantiles. In Robust Statistics, Data Analy sis and Computer Intensive Methods. Lecture Notes in Statist. 109. Springer, New York.

Koltchinskii, V. and Dudley, R. M. (1996). On spatial quantiles. Unpublished manuscript.

Koltchinskii, V. and Lang, L. (1996). A bootstrap test for spherical sy mmetry of a mutivariate distribution. Unpublished manuscript.

Mattner, L. (1992). Completness of location families, translated moments, and uniqueness of charges. Probab. Theory Related Fields 92 137-149.

Pollard, D. (1988). Asy mptotics for least absolute deviation regression estimators. Econometric Theory 7 186-199.

Py ke, R. (1975). Multidimensional empirical processes: some comments. In Stochastic Processes and Related Topics, Proceedings of the Summer Research Institute on Statistical Inference for Stochastic Processes 2 45-58. Academic Press, New York.

Py ke, R. (1985). Opportunities for set-indexed empirical and quantile processes in inference. In Bulletin of the International Statistical Institute: Proceedings of the 45th Session, Invited Papers 51 25.2.1-25.2.12. ISI, Voozburg, The Netherlands.

Reed, M. and Simon, B. (1975). Methods of Modern Mathematical physics. II. Fourier Analy sis, Self-Adjointness. Academic Press, New York.

Reiss, R.-D. (1989). Approximate Distribution of Order Statistics. Springer, New York.

Rockafellar, T. R. (1970). Convex Analy sis. Princeton Univ. Press.

Tukey, J. W. (1975). Mathematics and the picturing of data. In Proceedings of the International Congress of Mathematicians (R. D. James, ed.) 2 523-531. Canadian Math. Congress, Montreal.

Shorack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics. Wiley, New York.

Pollard, D. (1984). Convergence of Stochastic Processes. Springer, New York.

Pollard, D. (1990). Empirical Processes: Theory and Applications. IMS, Hay ward, CA.

Niemiro, W. (1992). Asy mptotics for M-estimators defined by convex minimization. Ann. Statist. 20 1514-1533.

Chaudhuri, P. (1991). Nonparametric estimates of regression quantiles and their local Bahadur representation. Ann. Statist. 19 760-777.

Chaudhuri, P. (1996). On a geometric notion of quantiles for multivariate data. J. Amer. Statist. Assoc. 91 862-872.

Eddy, W. F. (1985). Ordering of multivariate data. In Computer Science and Statistics: The Interface (L. Billard, ed.) 25-30. North-Holland, Amsterdam.

Koldobskii, A. (1990). Inverse problem for potentials of measures in Banach spaces. In Probability Theory and Mathematical Statistics (B. Grigelionis and J. Kubilius, eds.) 1 627-637. VSP/Mokslas. Koltchinskii, V. (1994a). Bahadur-Kiefer approximation for spatial quantiles. In Probability in Banach Spaces (J. Hoffmann-Jorgensen, J. Kuelbs and M. B. Marcus, eds.) 394-408. Birkh¨auser, Boston.

Milasevic, P. and Ducharme, G. R. (1987). Uniqueness of the spatial median. Ann. Statist. 15 1332-1333.

Rao, C. R. (1988). Methodology based on the L1 norm in statistical inference. Sankhy¯a Ser. A 50 289-313.

van der Vaart, A. W. and Wellner, J. (1996). Weak Convergence and Empirical Processes. Springer, New York.