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1、JamesE.GentleACompanionforMathematicalStatisticsACompanionforMathematicalStatisticsc2010JamesE.GentleACompanionforMathematicalStatisticsc2010JamesE.GentlePreface:MathematicalStatisticsAfterteachingmathematicalstatisticsforseveralyearsusingchalkonablack-board(and,later,smelly“dryerasem
2、arkers”onawhiteboard)mostlydoingproofsoftheorems,Idecidedtolecturefromcomputerslidesthatprovideanoutlineofthe“bigpicture”.Ratherthanspendclasstime“doing”proofsthataregiveninstandardtexts,Idecidedthattimewouldbebetterspentdis-cussingthematerialfromadifferent,higher-levelperspective.Ioft
3、endeviatefromthecannedslides,however,toaddressthedetailsofproofs,aswellasminutiaeofexamplesandothermaterialasIfeelnecessary,orasthestudentstellmeisnecessary.Afterwritingclassslides(inLATEX2ε,ofcourse),mostlyinbulletform,Ibeganwritingtextaroundthebullets,andIputthenotesontheclasswebsit
4、e.LaterIdecidedthatasingledocumentwithasubjectindex(seepages665through678)wouldbeusefultoserveasaCompanionforthestudyofmathematicalstatistics.Theotherbigdealaboutthisdocumentistheinternallinks,whichofcourseisnotsomethingthatcanbedonewithahardcopybook.(OnethingImustwarnyouaboutisthatth
5、ereisa(known)bugintheLATEXpackagehyperref;ifthereferencedpointhappenstooccuratthetopofapage,thelinktakesyoutothepreviouspage–soifyoudon’tseewhatyouexpect,trygoingtothenextpage.)Muchofthepresentdocumentreflectsitsoriginasclassroomnotes;itcontainsmanyincompletesentencesorsentencefragment
6、s,anditlackscon-nectivematerialinmanyplaces.(Theconnectivematerialwas(probably!)suppliedorallyduringthelectures.)Severalsectionsareincompleteandseveralproofsareomitted.Also,Iplantoaddmoreexamples.Ijusthavenothadtimetotypeupthematerial.Idonotrecommendthatyouprintthesenotes.Firstofall,t
7、heyareevolv-ing,soaprintedversionisjustasnapshot.Secondly,thePDFfilecontainsactiveinternallinks,sonavigationiseasy.(Forversionswithoutactivelinks,Itrytobefriendlytothereaderbyprovidingpagenumberswithmostinternalreferences.)ACompanionforMathematicalStatisticsc2010JamesE.GentleviPrefaceT
8、hisdo
