LEADER 03521nam 22006975 450 001 9910300157203321 005 20250411131602.0 010 $a3-319-04972-0 024 7 $a10.1007/978-3-319-04972-4 035 $a(CKB)3710000000119100 035 $a(Springer)9783319049724 035 $a(MH)014079061-6 035 $a(SSID)ssj0001247677 035 $a(PQKBManifestationID)11815505 035 $a(PQKBTitleCode)TC0001247677 035 $a(PQKBWorkID)11195538 035 $a(PQKB)11746122 035 $a(DE-He213)978-3-319-04972-4 035 $a(MiAaPQ)EBC6219464 035 $a(MiAaPQ)EBC1731016 035 $a(Au-PeEL)EBL1731016 035 $a(CaPaEBR)ebr10969024 035 $a(OCoLC)879645562 035 $a(PPN)178779199 035 $a(EXLCZ)993710000000119100 100 $a20140507d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStatistical Theory and Inference /$fby David J. Olive 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (XII, 434 p. 8 illus.)$conline resource 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-319-04971-2 327 $aProbability and Expectations.- Multivariate Distributions -- Exponential Families.- Sufficient Statistics.- Point Estimation I.-Point Estimation II -- Testing Statistical Hypotheses.- Large Sample Theory.- Confidence Intervals.- Some Useful Distributions -- Bayesian Methods -- Stuff for Students. 330 $aThis text is for  a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful  tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions. 606 $aStatistics 606 $aProbabilities 606 $aStatistics 606 $aStatistical Theory and Methods 606 $aProbability Theory 606 $aStatistics 615 0$aStatistics. 615 0$aProbabilities. 615 0$aStatistics. 615 14$aStatistical Theory and Methods. 615 24$aProbability Theory. 615 24$aStatistics. 676 $a519.24 700 $aOlive$b David J$4aut$4http://id.loc.gov/vocabulary/relators/aut$0525082 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300157203321 996 $aStatistical theory and inference$9822874 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress