Charles Joel Stone

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Charles Joel Stone
Born(1936-07-13)July 13, 1936
Los Angeles, California, U.S.
DiedApril 16, 2019(2019-04-16) (aged 82)
Alma mater
Spouse(s)
Barbara L. Sohn
​
(m. 1966)​
Children2
Scientific career
ThesisLimit Theorems for Birth and Death Processes and Diffusion Processes
Doctoral advisorSamuel Karlin
Doctoral students

Charles "Chuck" Joel Stone (July 13, 1936 – April 16, 2019) was an American statistician and mathematician.

Early life[]

Charles Joel Stone was born and raised in Los Angeles.[1] After secondary school at North Hollywood High School, Stone graduated with a Bachelor of Science in science from the California Institute of Technology in 1958.[2][3] He then matriculated at Stanford University, where in 1961 he received his PhD in statistics. His PhD thesis Limit Theorems for Birth and Death Processes and Diffusion Processes was supervised by Samuel Karlin.[4][5]

Career[]

From 1962 to 1964 Stone was an assistant professor in the mathematics department of Cornell University. From 1964 1981 to he was a faculty member of the mathematics department of UCLA (University of California, Los Angeles), where he worked extensively with Leo Breiman (who moved to Berkeley in 1980) and Sidney Charles Port (born 1935).[1] In the statistics department of the University of California, Berkeley, Stone was from 1981 a full professor, a position which he held until his retirement as professor emeritus.[3]

... in the early 1980s he wrote two landmark papers regarding optimal rates of convergence for statistical estimators. His results carefully took into account dependence on the dimensions of spaces in which predictors and outcomes lie, and the derivative being estimated.[3]

When they were professors at UCLA, Stone and Breiman consulted for Technology Services Corporation in Santa Monica. Based on their work, they co-authored a 1978 technical report, Parsimonious Binary Classification Trees, Elaborating on the report, in 1984 they published, with two more co-authors, Jerome H. Friedman and Richard Allen Oshlen (born 1942), a greatly expended version entitled Classification and Regression Trees.[3]

This book may be the single item for which Chuck is most remembered. Its algorithms are for “classification,” “probability class estimation,” and “regression.” They, and perhaps especially a computer program for their implementation, became known as CART. One of Chuck’s principal contributions to the technical report and to the book was “CART pruning,” an intricate scheme for validating the algorithms and enabling them to be computationally feasible with the computers widely available at the time of publication. The use of the graphs associated with mean-square error as it varies with complexity is now standard in many areas. The CART book was the first mathematically and computationally rigorous treatment of approaches which now are commonplace and have found wide application. It has many examples, real and contrived. Some of these examples have become benchmarks for subsequent technologies in the field of “machine learning”. The CART ideas are part of almost every serious statistical curriculum worldwide. There are numerous computer programs, available both freely and commercially, that incorporate extensions of CART.[3]

In addition to research on statistical algorithms, Stone did research on potential theory, "local limit theorems, weak convergence of stochastic processes, and renewal theory."[3]

A number of Chuck’s later efforts concerned log-splines and their applications to regression (including time series) and survival analysis. Many of the papers in this long series were co-authored. Among the co-authors are former students Charles Kooperberg (now of the University of Washington), Mark Hansen (of UC Davis), and Young Truong (of the University of North Carolina). A summary of that line of inquiry was the subject of Chuck’s Wald Lectures.[3]

Stone was the advisor for 14 doctoral students, including Probal Chaudhuri, Mark Henry Hansen, and James Stephen "Steve" Marron.[4] Stone was a Guggenheim Fellow for the academic year 1980–1981.[6] In 1986 he was an invited speaker at the International Congress of Mathematicians in Berkeley, California.[7] He was elected a Fellow of the Institute of Mathematical Statistics in 1970 [8] and a Fellow of the Class of 2013 (announced in 2012) of the American Mathematical Society. He was elected a Member of the National Academy of Sciences in 1993.[9]

Personal life[]

In June 1966 he married Barbara L. Sohn in Los Angeles. They had two sons.[3]

Death[]

Stone died on April 16, 2019.[3]

Selected publications[]

Articles[]

  • Stone, Charles (1963). "Weak convergence of stochastic processes defined on semi-infinite time intervals". Proceedings of the American Mathematical Society. 14 (5): 694. doi:10.1090/S0002-9939-1963-0153046-2. ISSN 0002-9939.
  • Stone, Charles (1965). "On characteristic functions and renewal theory". Transactions of the American Mathematical Society. 120 (2): 327. doi:10.1090/S0002-9947-1965-0189151-0. ISSN 0002-9947.
  • Stone, Charles (1967). "On local and ratio limit theorems". Lucien M. Le Cam; Jerzy Neyman, eds., Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 2: Contributions to Probability Theory, Part 2. University of California Press. pp. 217–224.
  • Port, Sidney C.; Stone, Charles J. (1967). "Hitting time and hitting places for non-lattice recurrent random walks". Journal of Mathematics and Mechanics. 17 (1): 35–57. JSTOR 24902152.
  • Port, Sidney C.; Stone, Charles J. (1969). "Potential theory of random walks on Abelian groups". Acta Mathematica. 122: 19–114. doi:10.1007/BF02392007. ISSN 0001-5962.
  • Port, Sidney C.; Stone, Charles J. (1971). "Infinitely divisible processes and their potential theory. I". Annales de l'Institut Fourier. 21 (2): 157–275. doi:10.5802/aif.376. ISSN 0373-0956.
  • Port, Sidney C.; Stone, Charles J. (1971). "Infinitely divisible processes and their potential theory. II". Annales de l'Institut Fourier. 21 (4): 179–265. doi:10.5802/aif.398. ISSN 0373-0956.
  • Stone, Charles J. (1972). "An upper bound for the renewal function". The Annals of Mathematical Statistics. 43 (6): 2050–2052. doi:10.1214/aoms/1177690883. JSTOR 2240223.
  • Stone, Charles J. (1975). "Adaptive Maximum Likelihood Estimators of a Location Parameter". The Annals of Statistics. 3 (2): 267–284. doi:10.1214/aos/1176343056. JSTOR 2958945.
  • Stone, Charles J. (1977). "Consistent nonparametric regression". The Annals of Statistics. 5 (4): 595–620. doi:10.1214/aos/1176343886. JSTOR 2958783.[10] (over 2300 citations)
  • Stone, Charles J. (1982). "Optimal Global Rates of Convergence for Nonparametric Regression". The Annals of Statistics. 10 (4): 1040–1053. doi:10.1214/aos/1176345969. JSTOR 2240707.
  • Stone, Charles J. (1984). "An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates". The Annals of Statistics. 12 (4): 1285–1297. doi:10.1214/aos/1176346792. JSTOR 2241002.
  • Stone, Charles J. (1990). "Large-Sample Inference for Log-Spline Models". The Annals of Statistics. 18 (2): 717–741. doi:10.1214/aos/1176347622. JSTOR 2242130.
  • Kooperberg, Charles; Stone, Charles J. (1991). "A study of logspline density estimation". Computational Statistics & Data Analysis. 12 (3): 327–347. doi:10.1016/0167-9473(91)90115-I.
  • Truong, Young K.; Stone, Charles J. (1992). "Nonparametric Function Estimation Involving Time Series". The Annals of Statistics. 20 (1): 77–97. doi:10.1214/aos/1176348513. JSTOR 2242151.
  • Stone, Charles J. (1994). "The Use of Polynomial Splines and Their Tensor Products in Multivariate Function Estimation". The Annals of Statistics. 22 (1): 118–171. JSTOR 2242446.
  • Kooperberg, Charles; Stone, Charles J.; Truong, Young K. (1995). "Hazard Regression". Journal of the American Statistical Association. 90 (429): 78–94. doi:10.1080/01621459.1995.10476491.
  • Kooperberg, Charles; Bose, Smarajit; Stone, Charles J. (1997). "Polychotomous Regression". Journal of the American Statistical Association. 92 (437): 117–127. doi:10.1080/01621459.1997.10473608.
  • Stone, Charles J.; Hansen, Mark H.; Kooperberg, Charles; Truong, Young K. (1997). "Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture". The Annals of Statistics. 25 (4). doi:10.1214/aos/1031594728.
  • Kooperberg, Charles; Bose, Smarajit; Stone, Charles J. (1997). "Polychotomous Regression". Journal of the American Statistical Association. 92 (437): 117–127. doi:10.1080/01621459.1997.10473608.
  • Stone, Charles J. (2005). "Nonparametric M-regression with free knot splines". Journal of Statistical Planning and Inference. 130 (1–2): 183–206. doi:10.1016/j.jspi.2003.05.002. ISSN 0378-3758.
  • Kooperberg, C.; Stone, C. J. (2013). "Chapter 16. Logspline Density Estimation". Nonlinear Estimation and Classification. Lecture Notes in Statistics, vol. 171. pp. 285–296. ISBN 9780387215792.

Books[]

  • Hoel, P.; Port, S. C.; Stone, C. J. (1971). Introduction to Probability Theory. Houghton Mifflin. (textbook)
  • Hoel, P.; Port, S. C.; Stone, C. J. (1971). Introduction to Statistics. Houghton Mifflin. (textbook)
  • Hoel, Paul G.; Port, Sidney C.; Stone, Charles J. (December 1986). Introduction to Stochastic Processes. Waveland Press. ISBN 9781478608998. 1st edition. Houghton Mifflin. 1971. (textbook)
  • Port, Sidney C.; Stone, Charles J. (December 2, 2012). Brownian Motion and Classical Potential Theory. Elsevier. ISBN 9780323159081. 1st edition. 1978.[11]
  • Breiman, Leo; Friedman, Jerome H.; Olshen, Richard A.; Stone, Charles J. (1984). Classification And Regression Trees (1st ed.).
    • Breiman, Leo; Friedman, Jerome H.; Olshen, Richard A.; Stone, Charles J. (2017). ebook. Boca Raton: Routledge. doi:10.1201/9781315139470. ISBN 9781315139470; 368 pages; abstract & table of contentsCS1 maint: postscript (link)
  • Stone, Charles J. (1996). A Course in Probability and Statistics. Duxbury Press. ISBN 9780534233280.

References[]

  1. ^ Jump up to: a b Stone, Charles J. (2010). "Selected recollections of my relationship with Leo Breiman" (PDF). The Annals of Applied Statistics. 4 (4). arXiv:1101.0941. doi:10.1214/10-AOAS431. S2CID 62578779.
  2. ^ "California Institute of Technology Sixth-fourth Annual Commencement Exercise" (PDF). California Institute of Technology. 1958. Retrieved July 25, 2021.
  3. ^ Jump up to: a b c d e f g h i Olshen, Richard A.; Bickel, Peter; Evans, Steven N. (2020). "In Memoriam. Charles Joel Stone, Professor of Statistics, Emeritus, UC Berkeley". Academic Senate, University of California.
  4. ^ Jump up to: a b Charles Joel Stone at the Mathematics Genealogy Project
  5. ^ "Charles Joel Stone". Alumni, Statistics Department, Stanford University.
  6. ^ "Charles J. Stone". John Simon Guggenheim Memorial Foundation.
  7. ^ Stone, C. J. (1986). "A nonparametric framework for statistical modelling". Proceedings of the International Congress of Mathematicians, August 3–11, 1986, Berkeley, California. 2. pp. 1052–1056.
  8. ^ "Stone, Charles J." Scientific Legacy Database, Institute of Mathematical Statistics.
  9. ^ "Charles J. Stone". Member Directory, National Academy of Sciences.
  10. ^ "In memoriam: Charles Stone". UCLA Mathematics. April 25, 2019.
  11. ^ Blumenthal, R. M. (1980). "Book Review: Brownian motion and classical potential theory". Bulletin of the American Mathematical Society. 2 (3): 477–480. doi:10.1090/S0273-0979-1980-14774-6.
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