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G. Wahba 485matrix is a rank p projection operator. The degrees of freedom for signal is animportant concept in linear and nonlinear nonparametric regression, and itwas a mistake to hide it inconspicuously in Wahba (1983). Later Brad Efron(2004) gave an alternative definition of degrees of freedom for signal. The definitionin Wahba (1983) depends only on the data; Efron’s is essentially anexpected value. Note that in (41.1),trace{A(λ)} =n∑i=1∂ŷ i∂y i,where ŷ i is the predicted value of y i . This definition can reasonably be appliedto a problem with a nonlinear forward operator (that is, that maps dataonto the predicted data) when the derivatives exist, and the randomized tracemethod is reasonable for estimating the degrees of freedom for signal, althoughcare should be taken concerning the size of δ. Even when the derivatives don’texist the randomized trace can be a reasonable way of getting at the degreesof freedom for signal; see, e.g., Wahba et al. (1995).41.1.5 Yuedong Wang, Chong Gu and smoothing splineANOVASometime in the late 80s or early 90s I heard Graham Wilkinson expoundon ANOVA (Analysis of Variance), where data was given on a regular d-dimensional grid, viz.y ijk , t ijk , i =1,...,I, j =1,...,J, k =1,...,K,for d = 3 and so forth. That is, the domain is the Cartesian product ofseveral one-dimensional grids. Graham was expounding on how fitting a modelfrom observations on such a domain could be described as set of orthogonalprojections based on averaging operators, resulting in main effects, two factorinteractions, etc. “Ah-ha” I thought, we should be able to do exactly samething and more where the domain is the Cartesian product T = T 1 ⊗···⊗T dof d arbitrary domains. We want to fit functions on T , with main effects(functions of one variable), two factor interactions (functions of two variables),and possibly more terms given scattered observations, and we just need todefine averaging operators for each T α .Brainstorming with Yuedong Wang and Chong Gu fleshed out the results.Let H α ,α =1,...,d be d RKHSs with domains T α , each H α containing theconstant functions. H = H 1 ⊗···⊗H d is an RKHS with domain T . For eachα =1,...,d,constructaprobabilitymeasuredµ α on T α ,withthepropertythat the symbol (E α f)(t), the averaging operator, defined by∫(E α f)(t) = f(t 1 ,...,t d )dµ α (t α ),T ( α)
486 Ah-ha momentis well defined and finite for every f ∈Hand t ∈T.Considerthedecompositionof the identity operator:I = ∏ α(E α +(I −E α )) = ∏ αE α + ∑ α(I −E α ) ∏ β≠αE β+ ∑ (I −E α )(I −E β ) ∏E γ + ···+ ∏ (I −E α ). (41.3)α
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ContentsPrefacexviiContributorsI Th
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viii15 We live in exciting times 15
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x24.6 Open areas for research . . .
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xii36 Buried treasures 405Michael A
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xiv45.3 Multi-phase inference . . .
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PrefaceStatistics is the science of
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PrefacexixPart V comprises seven ar
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xxiiNancy FlournoyUniversity of Mis
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Part IThe history of COPSS
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4 A brief history of COPSSOnchiota
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6 A brief history of COPSSThe items
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8 A brief history of COPSSTABLE 1.1
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10 A brief history of COPSSwomen of
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12 A brief history of COPSSTABLE 1.
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16 A brief history of COPSS1.4.3 Ge
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20 A brief history of COPSSFor more
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2Reminiscences of the Columbia Univ
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I. Olkin 25Bechhofer, Allan Birnbau
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I. Olkin 27Milton Sobel was the tea
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3AcareerinstatisticsHerman Chernoff
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H. Chernoff 31given three-day basic
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H. Chernoff 33Savage tried to defen
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H. Chernoff 35In working on an arti
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H. Chernoff 37measure the loss as t
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H. Chernoff 39ReferencesAlbert, A.E
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4“. . . how wonderful the field o
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D.R. Brillinger 43He went on to be
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D.R. Brillinger 45Tukey wrote many
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D.R. Brillinger 4718. Personal comm
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50 Unorthodox journey to statistics
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6Statistics before and after my COP
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P.J. Bickel 616.3.1 Imperial Colleg
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P.J. Bickel 63make. This was first
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P.J. Bickel 65We eventually develop
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P.J. Bickel 67school interest, biol
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P.J. Bickel 69ReferencesBean, D., B
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P.J. Bickel 71Meinshausen, N., Bick
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74 Accidental biostatistics profess
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84 Passion for statisticsme is its
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86 Passion for statisticsTheir Biom
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88 Passion for statisticsthe first
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90 Passion for statisticsIn my expe
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92 Passion for statistics8.5 Job an
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94 Passion for statisticsperiod. An
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96 Passion for statisticsNeyman, J.
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98 Reflections on a statistical car
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100 Reflections on a statistical ca
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110 Science mixes it up with statis
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11Lessons from a twisted career pat
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J.S. Rosenthal 119My math professor
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J.S. Rosenthal 121contrary, it null
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J.S. Rosenthal 123of statistical re
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J.S. Rosenthal 125be open to whatev
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J.S. Rosenthal 12711.4 Final though
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130 Promoting equityand fellowship
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132 Promoting equityevaluate such e
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134 Promoting equityfor equity. But
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136 Promoting equityAssistant Secre
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Part IIIPerspectives on the fieldan
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142 Statistics in service to the na
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154 Where are the majors? ArtBachel
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156 Where are the majors?References
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158 Exciting timesCritically, Efron
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160 Exciting timesIn general I find
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162 Exciting timesI entered the Uni
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164 Exciting times15.3.3 Joining th
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166 Exciting timesvariability of a
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168 Exciting timesHabemma, J.D.F.,
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16The bright future of applied stat
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R.A. Irizarry 173FIGURE 16.1Illustr
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R.A. Irizarry 17516.4 The bright fu
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17The road travelled: From statisti
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N. Chatterjee 179the Kaplan-Meyer e
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N. Chatterjee 18117.4 Genome-wide a
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N. Chatterjee 183by any means. I ju
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N. Chatterjee 185right information
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N. Chatterjee 187The risk of cancer
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190 Journey into genetics and genom
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19Reflections on women in statistic
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M.E. Thompson 205Pearson in England
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M.E. Thompson 207TABLE 19.1The 14 C
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M.E. Thompson 209time series, the s
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M.E. Thompson 211the founding Chair
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M.E. Thompson 21319.7 The current s
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M.E. Thompson 215Yarmie, A. (2003).
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218 “The whole women thing”seem
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220 “The whole women thing”of t
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222 “The whole women thing”on a
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224 “The whole women thing”20.5
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226 “The whole women thing”Ifin
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228 “The whole women thing”Lond
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230 Reflections on diversityas a st
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232 Reflections on diversityall of
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234 Reflections on diversityforce m
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22Why does statistics have two theo
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D.A.S. Fraser 23922.2 65 years and
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D.A.S. Fraser 241function is taken
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D.A.S. Fraser 24322.4 Inference for
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D.A.S. Fraser 245that record the ef
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D.A.S. Fraser 247variable that give
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D.A.S. Fraser 249simple scalar case
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D.A.S. Fraser 251DiCiccio, T.J. and
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23Conditioning is the issueJames O.
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J.O. Berger 255Pedagogical example:
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J.O. Berger 257The SRP does not say
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J.O. Berger 25923.5 Conditional fre
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J.O. Berger 261conditional error pr
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J.O. Berger 263others). If x is the
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J.O. Berger 265How does a frequenti
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24Statistical inference from aDemps
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A.P. Dempster 269tion is simply une
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A.P. Dempster 271As the world of st
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A.P. Dempster 273when the X i are a
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A.P. Dempster 27524.5 Nonparametric
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A.P. Dempster 277can easily happen
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A.P. Dempster 279ReferencesBorel,
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25Nonparametric BayesDavid B. Dunso
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D.B. Dunson 283troduced, providing
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D.B. Dunson 285els in spatial stati
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D.B. Dunson 287methods as also prov
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D.B. Dunson 289ing background, and
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D.B. Dunson 291Murray, J.S., Dunson
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294 Choosing default methodsimagine
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296 Choosing default methods(a) mat
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298 Choosing default methodspartial
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300 Choosing default methodsdirecti
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27Serial correlation and Durbin-Wat
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T.W. Anderson 305The characteristic
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T.W. Anderson 307Consider the seria
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28Anon-asymptoticwalkinprobabilitya
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P. Massart 311(at least for discret
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P. Massart 31328.2.2 Non-asymptopia
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P. Massart 315where P = sµ. In oth
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P. Massart 317Hence by Talagrand’
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P. Massart 319ReferencesAkaike, H.
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P. Massart 321Talagrand, M. (1995).
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324 The present’s futuredata. In
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326 The present’s futureTABLE 29.
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328 The present’s future124356981
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330 The present’s futuremethod, t
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332 The present’s futureFIGURE 29
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334 The present’s futureIchino, M
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336 Lessons in biostatistics30.2 It
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338 Lessons in biostatisticsprognos
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340 Lessons in biostatisticstime fo
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342 Lessons in biostatisticsmeaning
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344 Lessons in biostatistics75% to
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346 Lessons in biostatisticshistolo
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31AvignetteofdiscoveryNancy Flourno
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N. Flournoy 351FIGURE 31.1Incidence
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N. Flournoy 353FIGURE 31.3Mean resp
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N. Flournoy 355FIGURE 31.4Kaplan-Me
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N. Flournoy 357As the study proceed
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32Statistics and public health rese
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R.L. Prentice 36132.2 Public health
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R.L. Prentice 363from urinary excre
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R.L. Prentice 36532.5 Clinical tria
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R.L. Prentice 367Kaplan, E.L. and M
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370 Statistics in a new erative eff
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372 Statistics in a new eraular com
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374 Statistics in a new erajoint de
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376 Statistics in a new eraof the n
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378 Statistics in a new eraLai, T.L
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34Meta-analyses: Heterogeneity can
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N.M. Laird 383into the sum of a “
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N.M. Laird 385are “approximately
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N.M. Laird 387included in the major
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N.M. Laird 389Yusuf, S., Peto, R.,
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392 Good health: Statistical challe
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406 Buried treasuresmeasurement tec
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408 Buried treasuresIn a most rewar
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410 Buried treasureslems different
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37Survey sampling: Past controversi
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R.J. Little 41537.2 Probability or
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R.J. Little 417for the “design-ba
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R.J. Little 419estimate of variance
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R.J. Little 421Example 2 continued
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R.J. Little 42337.3.4 The design-mo
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R.J. Little 42537.5 ConclusionsI am
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R.J. Little 427Isaki, C.T. and Full
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38Environmental informatics: Uncert
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N. Cressie 431and conquer” strate
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N. Cressie 433In the last 20 years,
Page 456 and 457: N. Cressie 435Once the satellite ha
Page 458 and 459: N. Cressie 437FIGURE 38.1Locations
Page 460 and 461: N. Cressie 439regional and seasonal
Page 462 and 463: N. Cressie 441ciated with the spati
Page 464 and 465: N. Cressie 443is the set of all pix
Page 466 and 467: N. Cressie 445challenge is to devel
Page 468 and 469: N. Cressie 447Gourdji, S.M., Muelle
Page 470: N. Cressie 449Wikle, C.K., Milliff,
Page 473 and 474: 452 Statistical geneticsTABLE 39.1T
Page 475 and 476: 454 Statistical geneticsStewart, 19
Page 477 and 478: 456 Statistical geneticslocidata
Page 479 and 480: 458 Statistical geneticssufficientl
Page 481 and 482: 460 Statistical geneticsBrown, M.D.
Page 483 and 484: 462 Statistical geneticsLange, K. a
Page 485 and 486: 464 Statistical geneticsThompson, E
Page 487 and 488: 466 Targeted learningods for nonpar
Page 489 and 490: 468 Targeted learningdenote the obs
Page 491 and 492: 470 Targeted learningSuch an estima
Page 493 and 494: 472 Targeted learningliterature pro
Page 495 and 496: 474 Targeted learninglihood estimat
Page 497 and 498: 476 Targeted learning40.6 Some spec
Page 499 and 500: 478 Targeted learningmemory challen
Page 501 and 502: 480 Targeted learningvan der Laan,
Page 503 and 504: 482 Ah-ha momentwe have just seen.
Page 505: 484 Ah-ha momentthe data is unchang
Page 509 and 510: 488 Ah-ha momentit was something of
Page 511 and 512: 490 Ah-ha momentdefines a Euclidean
Page 513 and 514: 492 Ah-ha momentparticipate in the
Page 515 and 516: 494 Ah-ha momentLee, Y., Wahba, G.,
Page 518 and 519: 42In praise of sparsity and convexi
Page 520 and 521: R.J. Tibshirani 499TABLE 42.1Asampl
Page 522 and 523: R.J. Tibshirani 501CancerEpithelial
Page 524 and 525: R.J. Tibshirani 503that the error v
Page 526: R.J. Tibshirani 505Tibshirani, R.J.
Page 529 and 530: 508 Features of Big Dataproblems en
Page 531 and 532: 510 Features of Big Datalearning st
Page 533 and 534: 512 Features of Big Data1210(a)p =
Page 535 and 536: 514 Features of Big Data25002000150
Page 537 and 538: 516 Features of Big DataAs an illus
Page 539 and 540: 518 Features of Big Datafor some gi
Page 541 and 542: 520 Features of Big Data43.7.3 Prop
Page 543 and 544: 522 Features of Big DataBühlmann,
Page 546 and 547: 44Rise of the machinesLarry A. Wass
Page 548 and 549: L.A. Wasserman 527if an idea requir
Page 550 and 551: L.A. Wasserman 529●●●● ●
Page 552 and 553: L.A. Wasserman 531●●●●●
Page 554 and 555: L.A. Wasserman 533FIGURE 44.4Simula
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L.A. Wasserman 53544.7 Education an
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45Atrioofinferenceproblemsthatcould
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X.-L. Meng 539it is directly rooted
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X.-L. Meng 541exactly, but this doe
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X.-L. Meng 543That is, when we do n
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X.-L. Meng 545(a) For what classes
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X.-L. Meng 547subsequent analysts c
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X.-L. Meng 549can prove only that (
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X.-L. Meng 551In general, “What t
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X.-L. Meng 553vironmental progress
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X.-L. Meng 555which will be compare
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X.-L. Meng 557(a) Given partial kno
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X.-L. Meng 559AcknowledgementsThe m
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X.-L. Meng 561Knuth, D. (1997). The
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Part VAdvice for the nextgeneration
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566 Inspiration, aspiration, ambiti
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568 Inspiration, aspiration, ambiti
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47Personal reflections on the COPSS
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R.J. Carroll 573them is, by definit
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R.J. Carroll 575(Carroll, 2003). In
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R.J. Carroll 57747.8 After the Pres
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R.J. Carroll 579Carroll, R.J., Spie
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582 Publishing without perishingthe
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584 Publishing without perishingbeg
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586 Publishing without perishingme,
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588 Publishing without perishingalr
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590 Publishing without perishingpor
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49Converting rejections into positi
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D.B. Rubin 595This pair of submissi
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D.B. Rubin 597There are several les
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D.B. Rubin 599very sound article, w
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D.B. Rubin 60149.8 ConclusionIhaveb
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D.B. Rubin 603Rubin, D.B. (1972). A
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606 Importance of mentorstwice as t
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608 Importance of mentorsexperiment
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610 Importance of mentorsposition a
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612 Importance of mentors50.7 The t
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51Never ask for or give advice, mak
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T. Speed 617overly generous. Perhap
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T. Speed 619and for finding enjoyme
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622 Thirteen rules3. Waste a lot of
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