Mathematical Statistics by K. Knight Review by: C. Geyer Journal of the American Statistical Association, Vol. 96, No. 454 (Jun., 2001), p. 779 Published by: American Statistical Association Stable URL: http://www.jstor.org/stable/2670317 . Accessed: 14/06/2014 00:29 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp
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Book Reviews
779
Mathematical Statistics. K. KNIGHT, Boca Raton,FL: Chapmanand Hall/CRC,2000. ISBN 158488-178-X.iv + 473 pp. $49.95.
Towing Icebergs, Falling Dominoes and Other Adventures in Applied Mathematics. RobertB. BANKS, Princeton, NJ:Princeton University Press,1998.ISBN 0-691-05948-9.xi + 238 pp. $29.95.
KeithKnight'snew book is a welcomeadditionto textbooks appropriate As a statistician who has recentlymade a livingteachingstatisticsto formasters-level theorycourses.It is a ratherchallengingtext,muchmore engineering students, I have been on thelookoutforways to so thanthe books by Lindgren(1993) and Casella and Berger(1990), but undergraduate easierthanthe textof Bickel and Doksum(2000). The 211 "problemsand connectour fieldof studywiththephysicalworld.RobertBanks,an expeteacher,has apparently spentmuchof his careerdoing are mostlydifficult complements" (as indicatedby theircharacterization as riencedengineering "problems andcomplements"). Therearefewstraightforward "plugandchug" thesamething.In TowingIcebergs,FallingDominoesand OtherAdventures Banks presentsan entertaining collectionof physproblems ofthesortI ask mymaster's-level students on exams,suchas "What in AppliedMathematics, neededfortheirsolution.Some of the is var(X+ Y + Z) whenthevariancesand covariancesof X, Y, and Z are ical problemsand the mathematics and utilitarian, butall are forinstance, given?"Knight, asksforproofsoftheunivariate andmultivariate solutionsare elegantand othersare computational thought provoking. Jensen'sinequalities, thelatterrequiring thestudentto inventforherselfand in thisbook,onlya fewmakeuse of statistics Of theproblemspresented or something provetheseparating hyperplane theorem similar.Problemslike or probability in thesolution,buttheseare worthconsideration. In Chapter2, thisare too hardforourmaster's-level Thus I concludewithsome students. a studyof exponential and the growththatinvokesbothalligatorpopulations regret(and also withsome chagrin,since it worksforhimin Canada) that nationaldebt,readersare introduced to regression and correlation. Some of thisbookis toohardformostAmericanmaster'sdegreeprograms. To readers thelanguageand presentation mightmakea statistics teacheruneasy.As an who questionwhether such a judgmentshouldbe made solelyon thebasis r does not example,we knowthata highvalue of the samplecorrelation I can onlysay thatstudents of problems, learnwhattheinstructor exercises necessarily meanthata linearmodelis ideal,andthata relatively low valueof and testsand ignoretherest,so theproblemsare crucial.This book might r does notruleouta linearrelationship andthemeanof a betweena predictor be usablehereif theinstructor wroteand assigneda lotof easierproblems.I response.Such detailis losthere,butin theengineering contextperhapsthis mighttryit myselfsometime. is appropriate. The important thingthatthisbookhas to offeris a willingness Turning to Knight'scoverageoftopics,I finditexcellent.Beforegetting to to look at all of mathematics and statistics as a big toolbox. trotoutone ofmyfavorite details,letme first quotes,byPaul Halmos(1973), It is in considering thisset of toolsthatI believethisbook has a valuable lessonforengineers andstatistics teachersalike.Manyofthebook'sproblems Calculusbooksare bad becausethereis no suchsubjectas calculus;it can be vieweddeterministically usingmodelsthatinvokedifferential equais nota subjectbecauseit is manysubjects. tionsand physicalprinciples. The sameproblemscan be viewedstatistically timeseries,or nonparametric usingmethodssuch as regression, forecasting The same is trueof "theoretical statistics" or,stillworse,"theoretical probtechniques. The book's lastchapter, titled"How Fast Can RunnersRun?,"is whichis the subjectof thistextand its competitors. abilityand statistics," an intriguing thatuses differenapproachto thelimitsofhumanperformance and two-thirds Most suchbooks tial (The book is one-third probability statistics.) equationsto defineour abilityto accelerateand theforcesof resistance covera varietyof ratherold stuffwithno coherentstoryand leave students likefriction fromthetrackand deceleration of legs on impact.This thorough to readcurrent literature. ill-prepared statistical analysishelpspinpointthephysiological limitsof running without providing some newermaterial:MonteCarlo calculation,Op and muchin thewayof forecasting Knightintroduces howquicklyrecordswill improve. centrallimittheorems fordependent randomsequences,robustoP notation, Hereis a simpleassignment thatI ask of sophomore in theirfirst engineers M estimation, least medianof squaresregression, statistics ness,influence functions, course:Look through yourcalculusbook and finda wordproblem theEM algorithm, thatstrikesyou as completelyunrealistic.(This is not veryhard in most thejackknife,computeroptimization (Newton-Raphson, least squares),generalizedlinearmodels and quasi- texts.)Whatabouttheproblemmakesit unrealistic? iteratively reweighted new Althoughstudents It to statistics likelihood,highestposteriordensityregions,and Laplace approximation. do notalwayshave thelanguageto expressit well,theiranswer thesetopicsshouldor shouldnotbe cov- is usuallythatsomequantity is purelya matterof tastewhether thatis obviouslya variableis beingtreatedas a eredin thecourse(because"thereis no suchsubject"),butI preferKnight's constant. I know. in Applied TowingIcebergs,Falling Dominoes and OtherAdventures choiceof topicsoverothertextbooks is a good attempt of methto exposereadersto thewidevariety of Mathematics One of Knight'schoicesis especiallynotable.His is thebesttreatment Forstatistics thebook teachers, likelihoodtheorythatI knowat anylevel.Thereareproofsof theasymptotic ods availableto attackmanyappliedproblems. can provide problemsforwhichstudents of themaximumlikelihoodestimator normality (MLE) and thechi-squared providea good sourceof interesting to thesolutionspresented. I recommend thebook as supplements of the likelihoodratioteststatistic.He discussesobservedand statistical distribution who teachengineers, and can envisionit readingto statisticians and the"sandwichesti- background expectedFisherinformation, misspecified likelihood, students witha varianceof a misspecified mator"of asymptotic MLE. He givesa rigorous beinga good resourcefora modelingcourseformathematics in statistics. discussionof the asymptotic of maximumlikelihood(explaining background optimality
I wishI had a nickelfor and theHajek convolution superefficiency theorem). everytimeI have been asked forrecommended readingon likelihoodtheoryand had to say one did notexistat thislevel.Now I can wholeheartedly recommend Mathematical Statistics. C. GEYER University ofMinnesota
RickCLEARY CornellUniversity Empirical Processes in M-Estimation. Press, Sara A. VAN DE GEER. Cambridge, U.K.: CambridgeUniversity 2000. ISBN 0-521-65002-X.xii + 286 pp. $59.95.
This book providesa unifiedtreatment of theasymptotic theoryfornonM estimators, parametric usingthetheoryof empiricalprocesses.Particular and theleast squares Bickel,P. J., and Doksum,K. A. (2000), MathematicalStatistics,Vol. I, emphasisis placed on maximumlikelihoodestimators estimators. The book comprises12 chapters:Introduction; Notationand DefEnglewoodCliffs,NJ:Prentice-Hall. Consistency; initions; Uniform Laws of Large Numbers; First Applications: Casella,G., andBerger,R. L. (1990), Statistical Inference (2nded.), Belmont, Increments of EmpiricalProcesses;CentralLimitTheorems;Rates of ConCA: Brooks/Cole. vergenceforMaximumLikelihoodEstimators; The Non-I.I.D.Case; Ratesof Halmos,P. R. (1973), How to WriteMathematics, Providence, RI: American Convergence forLeastSquaresEstimators; PenaltiesandSieves;Some AppliMathematical Society. cationsto Semiparamteric Models; and M-Estimators. Lindgren, B. W. (1993), StatisticalTheory(4thed.),New York:Chapmanand The bookassumesno priorknowledgeofempiricalprocessesanddevelops Hall. theneededresultsin Chapters2, 3, 5, 6, and 8. The otherchapterscontain REFERENCES
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