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T.W. Anderson 307Consider the serial correlation of the residualsr = z⊤ Azz ⊤ z= u⊤ M ⊤ AMuu ⊤ M ⊤ Mu .The matrix M is idempotent, i.e., M m = M, and symmetric. Its latent rootsare 0 and 1 and it has rank n − k. Let the possibly nonzero roots of M ⊤ AMbe ν 1 ,...,ν n−k . There is an n × (n − k) matrixH such that H ⊤ H = I n−kand⎡⎤ν 1 0 ··· 0H ⊤ M ⊤ 0 ν 2 ··· 0AMH = ⎢ . . . . ⎥⎣ . . . . ⎦ .0 0 ··· ν n−kLet w = H ⊤ v.Thenn−k∑r = ν j wj2j=1Durbin and Watson prove that∑wj 2 ./n−kj=1λ j ≤ ν j ≤ λ j+k ,j ∈{1,...,n− k}.Definen−k∑r L = λ j wj2∑n−k∑wj 2 , r U = λ j+k wj2/n−k∑wj 2 ./n−kj=1 j=1j=1j=1Then r L ≤ r ≤ r U .The “bounds procedure” is the following. If the observed serial correlationis greater than rU ⋆ conclude that the hypothesis of no serial correlation of thedisturbances is rejected. If the observed correlation is less than rL ⋆ ,concludethat the hypothesis of no serial correlation of the disturbance is accepted.The interval (rL ⋆ ,r⋆ U ) is called “the zone of indeterminacy.” If the observedcorrelation falls in the interval (rL ⋆ ,r⋆ U ), the data are considered as not leadingto a conclusion.ReferencesAnderson, R.L. (1942). Distribution of the serial correlation coefficient. TheAnnals of Mathematical Statistics, 13:1–13.Anderson, R.L. and Anderson, T.W. (1950). Distribution of the circular serialcorrelation coefficient for residuals from a fitted Fourier series. The Annalsof Mathematical Statistics, 21:59–81.
308 Serial correlation and Durbin-Watson boundsAnderson, T.W. (1948). On the theory of testing serial correlation. SkandinaviskAktuarietidskrift, 31:88–116.Anderson, T.W. (1971). The Statistical Analysis of Time Series. Wiley,NewYork.Anderson, T.W. (2003). An Introduction to Multivariate Statistical Analysis,3rd edition. Wiley, New York.Chipman, J.S. (2011). Advanced Econometric Theory. Routledge,London.Durbin, J. and Watson, G.S. (1950). Testing for serial correlation in leastsquares regression. I. Biometrika, 37:409–428.Durbin, J. and Watson, G.S. (1951). Testing for serial correlation in leastsquares regression. II. Biometrika, 38:159–178.
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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:
Page 278 and 279: J.O. Berger 257The SRP does not say
Page 280 and 281: J.O. Berger 25923.5 Conditional fre
Page 282 and 283: J.O. Berger 261conditional error pr
Page 284 and 285: J.O. Berger 263others). If x is the
Page 286 and 287: J.O. Berger 265How does a frequenti
Page 288 and 289: 24Statistical inference from aDemps
Page 290 and 291: A.P. Dempster 269tion is simply une
Page 292 and 293: A.P. Dempster 271As the world of st
Page 294 and 295: A.P. Dempster 273when the X i are a
Page 296 and 297: A.P. Dempster 27524.5 Nonparametric
Page 298 and 299: A.P. Dempster 277can easily happen
Page 300 and 301: A.P. Dempster 279ReferencesBorel,
Page 302 and 303: 25Nonparametric BayesDavid B. Dunso
Page 304 and 305: D.B. Dunson 283troduced, providing
Page 306 and 307: D.B. Dunson 285els in spatial stati
Page 308 and 309: D.B. Dunson 287methods as also prov
Page 310 and 311: D.B. Dunson 289ing background, and
Page 312: D.B. Dunson 291Murray, J.S., Dunson
Page 315 and 316: 294 Choosing default methodsimagine
Page 317 and 318: 296 Choosing default methods(a) mat
Page 319 and 320: 298 Choosing default methodspartial
Page 321 and 322: 300 Choosing default methodsdirecti
Page 324 and 325: 27Serial correlation and Durbin-Wat
Page 326 and 327: T.W. Anderson 305The characteristic
Page 330 and 331: 28Anon-asymptoticwalkinprobabilitya
Page 332 and 333: P. Massart 311(at least for discret
Page 334 and 335: P. Massart 31328.2.2 Non-asymptopia
Page 336 and 337: P. Massart 315where P = sµ. In oth
Page 338 and 339: P. Massart 317Hence by Talagrand’
Page 340 and 341: P. Massart 319ReferencesAkaike, H.
Page 342: P. Massart 321Talagrand, M. (1995).
Page 345 and 346: 324 The present’s futuredata. In
Page 347 and 348: 326 The present’s futureTABLE 29.
Page 349 and 350: 328 The present’s future124356981
Page 351 and 352: 330 The present’s futuremethod, t
Page 353 and 354: 332 The present’s futureFIGURE 29
Page 355 and 356: 334 The present’s futureIchino, M
Page 357 and 358: 336 Lessons in biostatistics30.2 It
Page 359 and 360: 338 Lessons in biostatisticsprognos
Page 361 and 362: 340 Lessons in biostatisticstime fo
Page 363 and 364: 342 Lessons in biostatisticsmeaning
Page 365 and 366: 344 Lessons in biostatistics75% to
Page 367 and 368: 346 Lessons in biostatisticshistolo
Page 370 and 371: 31AvignetteofdiscoveryNancy Flourno
Page 372 and 373: N. Flournoy 351FIGURE 31.1Incidence
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Page 376 and 377: 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,
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N. Cressie 435Once the satellite ha
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N. Cressie 437FIGURE 38.1Locations
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N. Cressie 439regional and seasonal
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N. Cressie 441ciated with the spati
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N. Cressie 443is the set of all pix
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N. Cressie 445challenge is to devel
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N. Cressie 447Gourdji, S.M., Muelle
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N. Cressie 449Wikle, C.K., Milliff,
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452 Statistical geneticsTABLE 39.1T
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454 Statistical geneticsStewart, 19
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456 Statistical geneticslocidata
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458 Statistical geneticssufficientl
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460 Statistical geneticsBrown, M.D.
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462 Statistical geneticsLange, K. a
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464 Statistical geneticsThompson, E
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466 Targeted learningods for nonpar
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468 Targeted learningdenote the obs
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470 Targeted learningSuch an estima
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472 Targeted learningliterature pro
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474 Targeted learninglihood estimat
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476 Targeted learning40.6 Some spec
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478 Targeted learningmemory challen
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480 Targeted learningvan der Laan,
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482 Ah-ha momentwe have just seen.
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484 Ah-ha momentthe data is unchang
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486 Ah-ha momentis well defined and
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488 Ah-ha momentit was something of
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490 Ah-ha momentdefines a Euclidean
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492 Ah-ha momentparticipate in the
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494 Ah-ha momentLee, Y., Wahba, G.,
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42In praise of sparsity and convexi
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R.J. Tibshirani 499TABLE 42.1Asampl
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R.J. Tibshirani 501CancerEpithelial
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R.J. Tibshirani 503that the error v
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R.J. Tibshirani 505Tibshirani, R.J.
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508 Features of Big Dataproblems en
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510 Features of Big Datalearning st
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512 Features of Big Data1210(a)p =
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514 Features of Big Data25002000150
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516 Features of Big DataAs an illus
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518 Features of Big Datafor some gi
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520 Features of Big Data43.7.3 Prop
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522 Features of Big DataBühlmann,
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44Rise of the machinesLarry A. Wass
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L.A. Wasserman 527if an idea requir
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L.A. Wasserman 529●●●● ●
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L.A. Wasserman 531●●●●●
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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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