Statistical Science

A Conversation with Jon Wellner

Moulinath Banerjee and Richard J. Samworth

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Jon August Wellner was born in Portland, Oregon, in August 1945. He received his Bachelor’s degree from the University of Idaho in 1968 and his PhD degree from the University of Washington in 1975. From 1975 until 1983, he was an Assistant Professor and Associate Professor at the University of Rochester. In 1983, he returned to the University of Washington, and has remained at the UW as a faculty member since that time. Over the course of a long and distinguished career, Jon has made seminal contributions to a variety of areas including empirical processes, semiparametric theory and shape-constrained inference, and has co-authored a number of extremely influential books. He has been honored as the Le Cam lecturer by both the IMS (2015) and the French Statistical Society (2017). He is a Fellow of the IMS, the ASA and the AAAS, and an elected member of the International Statistical Institute. He has served as co-Editor of The Annals of Statistics (2001–2003) and Editor of Statistical Science (2010–2013), and President of IMS (2016–2017). In 2010, he was made a Knight of the Order of the Netherlands Lion. In his free time, Jon enjoys mountain climbing and backcountry skiing in the Cascades and British Columbia.

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Statist. Sci., Volume 33, Number 4 (2018), 633-651.

First available in Project Euclid: 29 November 2018

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Conversation empirical processes semiparametric theory shape-constrained inference University of Washington


Banerjee, Moulinath; Samworth, Richard J. A Conversation with Jon Wellner. Statist. Sci. 33 (2018), no. 4, 633--651. doi:10.1214/18-STS670.

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  • 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.
  • Banerjee, M. and Wellner, J. A. (2001). Likelihood ratio tests for monotone functions. Ann. Statist. 29 1699–1731.
  • 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.
  • Boucheron, S. and Massart, P. (2011). A high-dimensional Wilks phenomenon. Probab. Theory Related Fields 150 405–433.
  • Chernoff, H. (1964). Estimation of the mode. Ann. Inst. Statist. Math. 16 31–41.
  • Chernozhukov, V., Galichon, A., Hallin, M. and Henry, M. (2017). Monge–Kantorovich depth, quantiles, ranks and signs. Ann. Statist. 45 223–256.
  • 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 Series 55 101–107. IMS, Beachwood, OH.
  • 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.
  • Dümbgen, L., van de Geer, S. A., Veraar, M. C. and Wellner, J. A. (2010). Nemirovski’s inequalities revisited. Amer. Math. Monthly 117 138–160.
  • Gardner, R. J. (2002). The Brunn–Minkowski inequality. Bull. Amer. Math. Soc. (N.S.) 39 355–405.
  • Gill, R. D. (1989). Non- and semi-parametric maximum likelihood estimators and the von Mises method. I. Scand. J. Stat. 16 97–128.
  • 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.
  • Giné, E. and Zinn, J. (1984). Some limit theorems for empirical processes. Ann. Probab. 12 929–998.
  • Giné, E. and Zinn, J. (1990). Bootstrapping general empirical measures. Ann. Probab. 18 851–869.
  • Giné, E. and Zinn, J. (1991). Gaussian characterization of uniform Donsker classes of functions. Ann. Probab. 19 758–782.
  • Groeneboom, P. (1987). Asymptotics for interval censored observations. Technical Report No. 87-18, Dept. Mathematics, Univ. Amsterdam.
  • Groeneboom, P. (1989). Brownian motion with a parabolic drift and Airy functions. Probab. Theory Related Fields 81 79–109.
  • Groeneboom, P. (1991). Nonparametric maximum likelihood estimators for interval censoring and deconvolution. Technical Report No. 378, Dept. Statistics, Stanford Univ.
  • Groeneboom, P. and Jongbloed, G. (2014). Nonparametric Estimation Under Shape Constraints: Estimators, Algorithms and Asymptotics. Cambridge Series in Statistical and Probabilistic Mathematics 38. Cambridge Univ. Press, New York.
  • Groeneboom, P. and Jongbloed, G. (2018). Some developments in the theory of shape constrained inference. Statist. Sci. 473–492.
  • 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.
  • Groeneboom, P., Jongbloed, G. and Wellner, J. A. (2001b). Estimation of a convex function: Characterizations and asymptotic theory. Ann. Statist. 29 1653–1698.
  • 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.
  • Groeneboom, P. and Wellner, J. A. (1992). Information Bounds and Nonparametric Maximum Likelihood Estimation. DMV Seminar 19. Birkhäuser, Basel.
  • Hall, W. J. and Wellner, J. A. (1980). Confidence bands for a survival curve from censored data. Biometrika 67 133–143.
  • Hall, W. J. and Wellner, J. (1981). Mean residual life. In Statistics and Related Topics (Ottawa, Ont., 1980) 169–184. North-Holland, Amsterdam.
  • Jager, L. and Wellner, J. A. (2007). Goodness-of-fit tests via phi-divergences. Ann. Statist. 35 2018–2053.
  • Kiefer, J. and Wolfowitz, J. (1976). Asymptotically minimax estimation of concave and convex distribution functions. Z. Wahrsch. Verw. Gebiete 34 73–85.
  • 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.
  • 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.
  • Præstgaard, J. and Wellner, J. A. (1993). Exchangeably weighted bootstraps of the general empirical process. Ann. Probab. 21 2053–2086.
  • Read, A., Morrissey, J. D. and Reichardt, L. F. (1970). American Dhaulagiri Expedition—1969. Am. Alp. Club J. 17.
  • Shorack, G. R. and Wellner, J. A. (2009). Empirical Processes with Applications to Statistics. Classics in Applied Mathematics 59. SIAM, Philadelphia, PA.
  • van Zwet, W. R. (1980). A strong law for linear functions of order statistics. Ann. Probab. 8 986–990.
  • van der Vaart, A. (1991). On differentiable functionals. Ann. Statist. 19 178–204.
  • van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes: With Applications to Statistics. Springer, New York.
  • Wellner, J. A. (1977). A Glivenko–Cantelli theorem and strong laws of large numbers for functions of order statistics. Ann. Statist. 5 473–480.
  • Wellner, J. A. (1978). Limit theorems for the ratio of the empirical distribution function to the true distribution function. Z. Wahrsch. Verw. Gebiete 45 73–88.