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I. Olkin 27 Milton Sobel was the teaching assistant for the 111a course; Robert Bechofer and Allan Birnbaum were also TAs. I remember that Milton Sobel sat in on Wald’s class on analysis of variance. Because he was at least one year ahead of me I thought that he would have taken this course earlier. He said he did take it earlier but the course was totally different depending on who was teaching it. It was depressing to think that I would have to take every course twice! As the course progressed Wald ran out of subscripts and superscripts , and subsequently added some subscripts on the left-hand side. Wolfowitz recommended three books, and assigned homework from them: on the right-hand side, e.g., x kl ij (a) H. Cramér (1945): Mathematical Methods of Statistics (b) J.V. Uspensky (1937): Introduction to Mathematical Probability (c) S.S. Wilks (1943): Mathematical Statistics He mentioned references to Kolmogorov’s Foundation of Probability and the Lévy and Roth book Elements of Probability. Wolfowitz used the term “chance variables” and commented that the Law of Small Numbers should have been called the Law of Small Probabilities. As I look through the notes it is funny to see the old-fashioned factorial symbols ⌊n instead of n!. As I reread my notes it seems to me that this course was a rather simplified first course in probability. Some of the topics touched upon the use of independence, Markov chains, joint distributions, conditional distributions, Chebychev’s inequality, stochastic convergence (Slutsky’s theorem), Law of Large Numbers, convolutions, characteristic functions, Central Limit Theorem (with discussion of Lyapunov and Lindeberg conditions). I have a comment in which Wolfowitz notes an error in Cramér (p. 343): (a) if y 1 ,y 2 ,... is a sequence with ∑ y i = c i for all c and σ 2 (y i ) → 0 as i →∞, then p lim i→∞ (y i − c i )=0;(b)theconverseisnottrueinthatitmaybethat σ 2 (y i ) →∞and yet p lim(y i − c i ) = 0. The second basic course was 111b, taught by Wald. The topics included point estimation, consistency, unbiasedness, asymptotic variance, maximum likelihood, likelihood ratio tests, efficiency. This course was more mathematical than 111a in that there was more asymptotics. In terms of mathematical background I note that he used Lagrange multipliers to show that, for w 1 ,...,w n ∈ [0, 1], ∑ n i=1 w2 i /(∑ n i=1 w i) 2 is minimized when w i =1/n for all i ∈{1,...,n}. Apparently, convexity was not discussed. There is a derivation of the chi-square distribution that includes a discussion of orthogonal matrices. This is one of the standard proofs. Other topics include Schwarz inequality (but not used for the above minimization), and sufficiency. The second part of the course dealt with tests of hypotheses, with emphasis on the power function (Wald used the term “power curve”), acceptance sampling, and the OC curve. My Columbia days are now over 65 years ago, but I still remember them as exciting and an incubator for many friendships and collaborations.
28 Reminiscences from Columbia References Anderson, T.W. Jr. (1955). The Department of Mathematical Statistics. In A History of the Faculty of Political Science, Columbia, R.G. Hoxie, Ed. Columbia University Press, pp. 250–255. Olkin, I. and Sampson, A.R. (2001a). Hotelling, Harold (1895–1973). In International Encyclopedia of the Social & Behavioral Sciences (N.J. Smelser and P.B. Baltes, Eds.). Pergamon, Oxford, 6921– 6925. URL http://www.sciencedirect.com/science/article/pii/ B0080430767002631. Olkin, I. and Sampson, A.R. (2001b). Harold Hotelling. In Statisticians of the Centuries. Springer,NewYork,pp.454–458.
Page 2 and 3: Contents Preface xvii Contributors
Page 4 and 5: 9.3 Optimal experimental design . .
Page 6 and 7: 20 “The whole women thing” 217
Page 8 and 9: 31 A vignette of discovery 349 Nanc
Page 10 and 11: xiii 41 Statistical model building,
Page 12: 50.3 Harvard University — the ear
Page 15 and 16: xviii Past, Present, and Future of
Page 18 and 19: Contributors Theodore W. Anderson S
Page 20: Contributors xxiii Terry Speed Univ
Page 24 and 25: 1 AbriefhistoryoftheCommitteeof Pre
Page 26 and 27: I. Olkin 5 2. The Joint Committee o
Page 28 and 29: I. Olkin 7 1967, p. 48; April 1968,
Page 30 and 31: I. Olkin 9 1.3.1 The Visiting Lectu
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Page 40 and 41: I. Olkin 19 1.4.4 Elizabeth L. Scot
Page 42: Part II Reminiscences and personal
Page 45 and 46: 24 Reminiscences from Columbia the
Page 47: 26 Reminiscences from Columbia cess
Page 51 and 52: 30 A career in statistics problem,
Page 53 and 54: 32 A career in statistics Laborator
Page 55 and 56: 34 A career in statistics Bruno de
Page 57 and 58: 36 A career in statistics At Stanfo
Page 59 and 60: 38 A career in statistics A trip to
Page 61 and 62: 40 A career in statistics Chernoff,
Page 63 and 64: 42 Wonderful field of statistics 4.
Page 65 and 66: 44 Wonderful field of statistics th
Page 67 and 68: 46 Wonderful field of statistics No
Page 70 and 71: 5 An unorthodox journey to statisti
Page 72 and 73: J.P. Shaffer 51 with enough full-ti
Page 74 and 75: J.P. Shaffer 53 piece of bad advice
Page 76 and 77: J.P. Shaffer 55 Asimpleexampleisthe
Page 78: J.P. Shaffer 57 Robinson, D. (2005)
Page 81 and 82: 60 Statistics before and after COPS
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Page 96 and 97: D.J. Brogan 75 my prepared exam and
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D.J. Brogan 77 7.5 Master’s degre
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D.J. Brogan 79 7.9 Job offers — f
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D.J. Brogan 81 I would be analyzing
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8 Developing a passion for statisti
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B.G. Lindsay 85 8.2 The first stati
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B.G. Lindsay 87 ture. In the so-cal
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B.G. Lindsay 89 My first PhD invest
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B.G. Lindsay 91 he would humor me.
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B.G. Lindsay 93 I nor my advisors k
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B.G. Lindsay 95 References Bahadur,
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9 Reflections on a statistical care
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R.D. Cook 99 recommendation to the
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R.D. Cook 101 no one sought my acqu
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R.D. Cook 103 that is, Y X|P S X?Su
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R.D. Cook 105 variance reduction de
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R.D. Cook 107 in an application can
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10 Science mixes it up with statist
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K. Roeder 111 10.3 Some collaborati
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K. Roeder 113 lations varied strong
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K. Roeder 115 Since that year (1997
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118 Lessons from a twisted career p
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12 Promoting equity Mary W. Gray De
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M.W. Gray 131 the kit and its refin
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M.W. Gray 133 of law and it was eas
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M.W. Gray 135 the mathematical scie
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M.W. Gray 137 References Affordable
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13 Statistics in service to the nat
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S.E. Fienberg 143 13.2 The National
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S.E. Fienberg 145 between the acade
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S.E. Fienberg 147 that have now bee
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S.E. Fienberg 149 computed the area
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S.E. Fienberg 151 Fienberg, S.E. (1
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14 Where are the majors? Iain M. Jo
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I.M. Johnstone 155 The NCES data sh
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15 We live in exciting times Peter
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P.G. Hall 159 15.2 Living with chan
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P.G. Hall 161 Some of this work is
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P.G. Hall 163 had some connection t
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P.G. Hall 165 a nonparametric funct
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P.G. Hall 167 References Abramowitz
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P.G. Hall 169 Pitman, E.J.G. (1938)
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172 Bright future of applied statis
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178 The road travelled also to help
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180 The road travelled gene-environ
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182 The road travelled given marker
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184 The road travelled future whole
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186 The road travelled Jugurnauth-L
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18 Ajourneyintostatisticalgeneticsa
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X. Lin 191 Ilearnedwhilemakingmyjou
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X. Lin 193 these simple methods in
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X. Lin 195 0’s. The association b
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X. Lin 197 expression, respectively
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X. Lin 199 skills through seminars,
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X. Lin 201 Pearl, J. (2001). Direct
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204 Women in statistics in Canada m
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206 Women in statistics in Canada I
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208 Women in statistics in Canada A
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210 Women in statistics in Canada T
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212 Women in statistics in Canada A
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214 Women in statistics in Canada R
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20 “The whole women thing” Nanc
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N.M. Reid 219 et al., 2012a), and t
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N.M. Reid 221 2% to all female facu
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N.M. Reid 223 Aparalleltothiscouldb
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N.M. Reid 225 Happily for most read
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N.M. Reid 227 Billard, L. and Ferbe
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21 Reflections on diversity Louise
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L.M. Ryan 231 would never have even
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L.M. Ryan 233 21.4 Gender issues I
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Part IV Reflections on the discipli
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238 Statistics’ two theories Viox
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240 Statistics’ two theories cont
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242 Statistics’ two theories wher
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244 Statistics’ two theories all
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246 Statistics’ two theories a ca
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248 Statistics’ two theories Freq
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250 Statistics’ two theories Ackn
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252 Statistics’ two theories Mars
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254 Conditioning is the issue The p
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256 Conditioning is the issue which
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258 Conditioning is the issue athou
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260 Conditioning is the issue Haar
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262 Conditioning is the issue TABLE
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264 Conditioning is the issue test
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266 Conditioning is the issue Birnb
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268 DS perspective on statistical i
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282 Nonparametric Bayes the meaning
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284 Nonparametric Bayes Prior (25.1
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286 Nonparametric Bayes perhaps one
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288 Nonparametric Bayes works well
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290 Nonparametric Bayes of Statisti
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26 How do we choose our default met
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A. Gelman 295 and in the first cour
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A. Gelman 297 distribution is a pow
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A. Gelman 299 sampling) yet has bec
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A. Gelman 301 Gelman, A. and Shaliz
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304 Serial correlation and Durbin-W
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310 Anon-asymptoticwalk ics, statis
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312 Anon-asymptoticwalk γ(t, x) =
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314 Anon-asymptoticwalk 28.2.3 Empi
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316 Anon-asymptoticwalk to Cirel’
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318 Anon-asymptoticwalk 28.4 Beyond
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320 Anon-asymptoticwalk Boucheron,
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29 The past’s future is now: What
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L. Billard 325 bounce around, so th
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L. Billard 327 TABLE 29.1 Airline d
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L. Billard 329 6 5 9 3 10 8 2 4 7 1
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L. Billard 331 FIGURE 29.5 PCA base
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L. Billard 333 References Bickel, P
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30 Lessons in biostatistics Norman
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N.E. Breslow 337 most of its statis
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N.E. Breslow 339 from complete remi
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N.E. Breslow 341 transplant and tho
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N.E. Breslow 343 TABLE 30.1 Regress
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N.E. Breslow 345 30.5 Conclusion Th
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N.E. Breslow 347 Partin, A.W., Yoo,
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350 A vignette of discovery Early a
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352 A vignette of discovery that in
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354 A vignette of discovery observa
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356 A vignette of discovery TABLE 3
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358 A vignette of discovery ciate t
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360 Statistics and public health re
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33 Statistics in a new era for fina
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T.L. Lai 371 (Rush et al., 2004) th
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T.L. Lai 373 (2012). The monograph
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T.L. Lai 375 loss function and assu
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T.L. Lai 377 References Ait-Sahalia
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T.L. Lai 379 Salmon, F. (2012). The
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382 Meta-analyses and heterogeneity
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35 Good health: Statistical challen
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A.S. Whittemore 393 form a useful f
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A.S. Whittemore 395 variate values.
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A.S. Whittemore 397 the observed fl
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A.S. Whittemore 399 represented, fo
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A.S. Whittemore 401 Consider, for e
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A.S. Whittemore 403 Venter, D.J., W
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36 Buried treasures Michael A. Newt
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M.A. Newton 407 F
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M.A. Newton 409 When measured at se
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M.A. Newton 411 Mason, D.M. and New
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414 Survey sampling clustering. Ano
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416 Survey sampling objective is th
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418 Survey sampling Estimators ̂q
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420 Survey sampling against model m
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422 Survey sampling wrong, so can w
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424 Survey sampling good design-bas
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426 Survey sampling Box, G.E.P. (19
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428 Survey sampling Rubin, D.B. (19
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430 Environmental informatics Hasti
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432 Environmental informatics this
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434 Environmental informatics the d
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436 Environmental informatics satel
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438 Environmental informatics The m
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440 Environmental informatics The c
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442 Environmental informatics FIGUR
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444 Environmental informatics 38.6
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446 Environmental informatics error
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448 Environmental informatics McLac
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39 Ajourneywithstatisticalgenetics
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E.A. Thompson 453 Population Meiosi
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E.A. Thompson 455 TABLE 39.2 The ch
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E.A. Thompson 457 39.5 The 2000s: A
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E.A. Thompson 459 I have given many
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E.A. Thompson 461 Fisher, R.A. (192
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E.A. Thompson 463 Schena, M., Shalo
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40 Targeted learning: From MLE to T
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M. van der Laan 467 confidence inte
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M. van der Laan 469 40.2.3 Target q
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M. van der Laan 471 the doubly cens
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M. van der Laan 473 40.4 Super lear
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M. van der Laan 475 has the general
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M. van der Laan 477 should also be
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M. van der Laan 479 Petersen, M. an
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41 Statistical model building, mach
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G. Wahba 483 geometrical argument c
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G. Wahba 485 matrix is a rank p pro
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G. Wahba 487 as proposed by Vapnik
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G. Wahba 489 details. In Corrada Br
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G. Wahba 491 As is easy to see here
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G. Wahba 493 ceedings of the Nation
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G. Wahba 495 Vapnik, V. (1995). The
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498 Sparsity and convexity . ^
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500 Sparsity and convexity recover
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502 Sparsity and convexity
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504 Sparsity and convexity Referenc
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43 Features of Big Data and sparses
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J. Fan 509 chemotherapy is helpful
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J. Fan 511 Realizations of two inde
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J. Fan 513 selection of genes or SN
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J. Fan 515 6 5 4 3 2 1 0 0
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J. Fan 517 4 (a) m=2 10 (b) m=100 2
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J. Fan 519 where · denotes the com
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J. Fan 521 43.8 Conclusion Big Data
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J. Fan 523 Hall, P., Titterington,
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526 Rise of the machines ric regres
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528 Rise of the machines ●●●
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530 Rise of the machines 44.4.2 Cas
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532 Rise of the machines is that th
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534 Rise of the machines FIGURE 44.
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536 Rise of the machines Acknowledg
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538 NP-hard inference seem to appre
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540 NP-hard inference signal or noi
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542 NP-hard inference In the strict
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544 NP-hard inference over equivale
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546 NP-hard inference large to pass
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548 NP-hard inference To illustrate
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550 NP-hard inference model P Y (Y
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552 NP-hard inference and accepted
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554 NP-hard inference Here let us a
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556 NP-hard inference The (middle)
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558 NP-hard inference understanding
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560 NP-hard inference Bouman, P., M
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562 NP-hard inference Nason, G.P. (
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46 Inspiration, aspiration, ambitio
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C.F.J. Wu 567 works, he wrote of Pe
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C.F.J. Wu 569 you will become, can
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572 Personal reflections on the COP
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48 Publishing without perishing and
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M. Davidian 583 tion research. He w
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M. Davidian 585 it accessible to pr
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M. Davidian 587 emphasized the impo
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M. Davidian 589 s/he needs to have
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M. Davidian 591 enjoy what you do,
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594 Converting rejections especiall
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596 Converting rejections decent su
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598 Converting rejections say, espe
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600 Converting rejections final ana
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602 Converting rejections Anderson,
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50 The importance of mentors Donald
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D.B. Rubin 607 earlier). Wheeler wa
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D.B. Rubin 609 program at Harvard,
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D.B. Rubin 611 50.6 Interim time in
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D.B. Rubin 613 my colleagues and st
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616 Never ask for or give advice su
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618 Never ask for or give advice yo
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52 Thirteen rules Bradley Efron Dep
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