×

A conversation with Jon Wellner. (English) Zbl 1407.01015


MSC:

01A70 Biographies, obituaries, personalia, bibliographies
62-03 History of statistics
62G05 Nonparametric estimation

Biographic References:

Wellner, Jon
PDFBibTeX XMLCite
Full Text: DOI arXiv Euclid

References:

[1] Balabdaoui, F., Rufibach, K. and Wellner, J. A. (2009). Limit distribution theory for maximum likelihood estimation of a log-concave density. Ann. Statist.37 1299-1331. · Zbl 1160.62008 · doi:10.1214/08-AOS609
[2] Banerjee, M. and Wellner, J. A. (2001). Likelihood ratio tests for monotone functions. Ann. Statist.29 1699-1731. · Zbl 1043.62037 · doi:10.1214/aos/1015345959
[3] Begun, J. M., Hall, W. J., Huang, W.-M. and Wellner, J. A. (1983). Information and asymptotic efficiency in parametric-nonparametric models. Ann. Statist.11 432-452. · Zbl 0526.62045 · doi:10.1214/aos/1176346151
[4] Boucheron, S. and Massart, P. (2011). A high-dimensional Wilks phenomenon. Probab. Theory Related Fields150 405-433. · Zbl 1230.62072 · doi:10.1007/s00440-010-0278-7
[5] Chernoff, H. (1964). Estimation of the mode. Ann. Inst. Statist. Math.16 31-41. · Zbl 0212.21802 · doi:10.1007/BF02868560
[6] Chernozhukov, V., Galichon, A., Hallin, M. and Henry, M. (2017). Monge-Kantorovich depth, quantiles, ranks and signs. Ann. Statist.45 223-256. · Zbl 1426.62163 · doi:10.1214/16-AOS1450
[7] Dümbgen, L., Rufibach, K. and Wellner, J. A. (2007). Marshall’s lemma for convex density estimation. In Asymptotics: Particles, Processes and Inverse Problems. Institute of Mathematical Statistics Lecture Notes—Monograph Series55 101-107. IMS, Beachwood, OH. · Zbl 1176.62029
[8] Dümbgen, L., Wellner, J. A. and Wolff, M. (2016). A law of the iterated logarithm for Grenander’s estimator. Stochastic Process. Appl.126 3854-3864. · Zbl 1351.60032 · doi:10.1016/j.spa.2016.04.012
[9] Dümbgen, L., van de Geer, S. A., Veraar, M. C. and Wellner, J. A. (2010). Nemirovski’s inequalities revisited. Amer. Math. Monthly117 138-160. · Zbl 1213.60039 · doi:10.4169/000298910x476059
[10] Gardner, R. J. (2002). The Brunn-Minkowski inequality. Bull. Amer. Math. Soc. (N.S.) 39 355-405. · Zbl 1019.26008 · doi:10.1090/S0273-0979-02-00941-2
[11] Gill, R. D. (1989). Non- and semi-parametric maximum likelihood estimators and the von Mises method. I. Scand. J. Stat.16 97-128. · Zbl 0688.62026
[12] Gill, R. D., Vardi, Y. and Wellner, J. A. (1988). Large sample theory of empirical distributions in biased sampling models. Ann. Statist.16 1069-1112. · Zbl 0668.62024 · doi:10.1214/aos/1176350948
[13] Giné, E. and Zinn, J. (1984). Some limit theorems for empirical processes. Ann. Probab.12 929-998. · Zbl 0553.60037
[14] Giné, E. and Zinn, J. (1990). Bootstrapping general empirical measures. Ann. Probab.18 851-869. · Zbl 0706.62017 · doi:10.1214/aop/1176990862
[15] Giné, E. and Zinn, J. (1991). Gaussian characterization of uniform Donsker classes of functions. Ann. Probab.19 758-782. · Zbl 0734.60007 · doi:10.1214/aop/1176990450
[16] Groeneboom, P. (1989). Brownian motion with a parabolic drift and Airy functions. Probab. Theory Related Fields81 79-109.
[17] Groeneboom, P. and Jongbloed, G. (2014). Nonparametric Estimation Under Shape Constraints: Estimators, Algorithms and Asymptotics. Cambridge Series in Statistical and Probabilistic Mathematics38. Cambridge Univ. Press, New York. · Zbl 1338.62008
[18] Groeneboom, P. and Jongbloed, G. (2018). Some developments in the theory of shape constrained inference. Statist. Sci. 473-492. · Zbl 1407.62108
[19] Groeneboom, P., Jongbloed, G. and Wellner, J. A. (2001a). A canonical process for estimation of convex functions: The “invelope” of integrated Brownian motion \(+t^4\). Ann. Statist.29 1620-1652. · Zbl 1043.62026 · doi:10.1214/aos/1015345957
[20] Groeneboom, P., Jongbloed, G. and Wellner, J. A. (2001b). Estimation of a convex function: Characterizations and asymptotic theory. Ann. Statist.29 1653-1698. · Zbl 1043.62027 · doi:10.1214/aos/1015345958
[21] Groeneboom, P., Lalley, S. and Temme, N. (2015). Chernoff’s distribution and differential equations of parabolic and Airy type. J. Math. Anal. Appl.423 1804-1824. · Zbl 1382.60106 · doi:10.1016/j.jmaa.2014.10.051
[22] Groeneboom, P. and Wellner, J. A. (1992). Information Bounds and Nonparametric Maximum Likelihood Estimation. DMV Seminar19. Birkhäuser, Basel. · Zbl 0757.62017
[23] Hall, W. J. and Wellner, J. A. (1980). Confidence bands for a survival curve from censored data. Biometrika67 133-143. · Zbl 0423.62078 · doi:10.1093/biomet/67.1.133
[24] Hall, W. J. and Wellner, J. (1981). Mean residual life. In Statistics and Related Topics (Ottawa, Ont., 1980) 169-184. North-Holland, Amsterdam.
[25] Jager, L. and Wellner, J. A. (2007). Goodness-of-fit tests via phi-divergences. Ann. Statist.35 2018-2053. · Zbl 1126.62030 · doi:10.1214/0009053607000000244
[26] Kiefer, J. and Wolfowitz, J. (1976). Asymptotically minimax estimation of concave and convex distribution functions. Z. Wahrsch. Verw. Gebiete34 73-85. · Zbl 0354.62035 · doi:10.1007/BF00532690
[27] Koltchinskii, V., Nickl, R., van de Geer, S. and Wellner, J. A. (2016). The mathematical work of Evarist Giné. Butl. Soc. Catalana Mat.31 5-29, 91. · Zbl 1376.01013
[28] Marshall, A. W. (1970). Discussion of: Asymptotic properties of isotonic estimators for the generalized failure rate function. I. Strong consistency, by Barlow, R. E. and van Zwet, W. R. In Nonparametric Techniques in Statistical Inference (Proc. Sympos., Indiana Univ., Bloomington, Ind., 1969) 174-176. Cambridge Univ. Press, London.
[29] Præstgaard, J. and Wellner, J. A. (1993). Exchangeably weighted bootstraps of the general empirical process. Ann. Probab.21 2053-2086. · Zbl 0792.62038 · doi:10.1214/aop/1176989011
[30] Read, A., Morrissey, J. D. and Reichardt, L. F. (1970). American Dhaulagiri Expedition—1969. Am. Alp. Club J.17.
[31] Shorack, G. R. and Wellner, J. A. (2009). Empirical Processes with Applications to Statistics. Classics in Applied Mathematics59. SIAM, Philadelphia, PA. · Zbl 1171.62057
[32] van Zwet, W. R. (1980). A strong law for linear functions of order statistics. Ann. Probab.8 986-990. · Zbl 0448.60025 · doi:10.1214/aop/1176994626
[33] van der Vaart, A. (1991). On differentiable functionals. Ann. Statist.19 178-204. · Zbl 0732.62035 · doi:10.1214/aos/1176347976
[34] van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes: With Applications to Statistics. Springer, New York. · Zbl 0862.60002
[35] Wellner, J. A. (1977). A Glivenko-Cantelli theorem and strong laws of large numbers for functions of order statistics. Ann. Statist.5 473-480. · Zbl 0365.62045 · doi:10.1214/aos/1176343844
[36] Wellner, J. A. (1978). Limit theorems for the ratio of the empirical distribution function to the true distribution function. Z. Wahrsch. Verw. Gebiete45 73-88. · Zbl 0382.60031 · doi:10.1007/BF00635964
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.