MARC record from Internet Archive

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024 7 $a10.1007/978-3-642-39909-1$2doi
035 $a(OCoLC)894040081
037 $acom.springer.onix.9783642399091$bSpringer Nature
050 4 $aQA276
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100 1 $aSpokoiny, V. G.,$eauthor.
245 10 $aBasics of modern mathematical statistics /$cVladimir Spokoiny, Thorsten Dickhaus.
264 1 $aBerlin :$bSpringer,$c[2014]
264 4 $c©2015
300 $a1 online resource
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
490 1 $aSpringer texts in statistics
504 $aIncludes bibliographical references.
588 0 $aPrint version record.
505 0 $aIntro; Preface; Preface of the First Author; Preface of the Second Author; Acknowledgments; Contents; 1 Basic Notions; 1.1 Example of a Bernoulli Experiment; 1.2 Least Squares Estimation in a Linear Model; 1.3 General Parametric Model; 1.4 Statistical decision problem. Loss and Risk; 1.5 Efficiency; 2 Parameter Estimation for an i.i.d. Model; 2.1 Empirical Distribution: Glivenko-Cantelli Theorem; 2.2 Substitution Principle: Method of Moments; 2.2.1 Method of Moments: Univariate Parameter; 2.2.2 Method of Moments: Multivariate Parameter; 2.2.3 Method of Moments: Examples
505 8 $a2.5.1 Kullback-Leibler Divergence2.5.2 Hellinger Distance; 2.5.3 Regularity and the Fisher Information: Univariate Parameter; 2.5.4 Local Properties of the Kullback-Leibler Divergence and Hellinger Distance; 2.6 Cramér-Rao Inequality; 2.6.1 Univariate Parameter; 2.6.2 Exponential Families and R-Efficiency; 2.7 Cramér-Rao Inequality: Multivariate Parameter; 2.7.1 Regularity and Fisher Information: MultivariateParameter; 2.7.2 Local Properties of the Kullback-Leibler Divergence and Hellinger Distance; 2.7.3 Multivariate Cramér-Rao Inequality; 2.7.4 Exponential Families and R-Efficiency
505 8 $a2.10 Quasi Maximum Likelihood Approach2.10.1 LSE as Quasi Likelihood Estimation; 2.10.2 LAD and Robust Estimation as Quasi Likelihood Estimation; 2.11 Univariate Exponential Families; 2.11.1 Natural Parametrization; 2.11.1.1 Some Properties of an EFn; 2.11.1.2 MLE and Maximum Likelihood for an EFn; 2.11.2 Canonical Parametrization; 2.11.2.1 Some Properties of an EFc; 2.11.2.2 Maximum Likelihood Estimation for an EFc; 2.11.3 Deviation Probabilities for the Maximum Likelihood; 2.11.3.1 Deviation Bound for Other Parameterizations; 2.11.3.2 Asymptotic Against Likelihood-Based Approach
520 3 $aThis textbook provides a unified and self-contained presentation of the main approaches to and ideas of mathematical statistics. It collects the basic mathematical ideas and tools needed as a basis for more serious studies or even independent research in statistics. The majority of existing textbooks in mathematical statistics follow the classical asymptotic framework. Yet, as modern statistics has changed rapidly in recent years, new methods and approaches have appeared. The emphasis is on finite sample behavior, large parameter dimensions, and model misspecifications. The present book provides a fully self-contained introduction to the world of modern mathematical statistics, collecting the basic knowledge, concepts and findings needed for doing further research in the modern theoretical and applied statistics. This textbook is primarily intended for graduate and postdoc students and young researchers who are interested in modern statistical methods.
650 0 $aMathematical statistics.
650 0 $aMathematics.
650 0 $aStatistics.
650 12 $aMathematics
650 12 $aStatistics as Topic
650 6 $aMathématiques.
650 6 $aStatistiques.
650 7 $aMathematical statistics.$2fast$0(OCoLC)fst01012127
653 00 $awaarschijnlijkheid
653 00 $aprobability
653 00 $astatistiek
653 00 $astatistics
653 00 $acomputerwetenschappen
653 00 $acomputer sciences
653 00 $astatistische analyse
653 00 $astatistical analysis
653 10 $aStatistics (General)
653 10 $aStatistiek (algemeen)
655 0 $aElectronic books.
655 4 $aElectronic books.
700 1 $aDickhaus, Thorsten,$eauthor.
776 08 $iPrint version:$aSpokoiny, V.G.$tBasics of modern mathematical statistics$z9783642399084$w(OCoLC)887942119
830 0 $aSpringer texts in statistics.
856 40 $3Scholars Portal$uhttp://books.scholarsportal.info/viewdoc.html?id=/ebooks/ebooks3/springer/2014-12-11/1/9783642399091
856 40 $3SpringerLink$uhttps://doi.org/10.1007/978-3-642-39909-1
856 40 $3SpringerLink$uhttps://link.springer.com/book/10.1007/978-3-642-39909-1
856 40 $3SpringerLink$uhttps://link.springer.com/book/10.1007/978-3-642-39908-4
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856 40 $3ProQuest Ebook Central$uhttps://public.ebookcentral.proquest.com/choice/publicfullrecord.aspx?p=6312867
880 8 $6505-00/(S$a2.2.3.1 Gaussian Shift2.2.3.2 Univariate Normal Distribution; 2.2.3.3 Uniform Distribution on [0,θ]; 2.2.3.4 Bernoulli or Binomial Model; 2.2.3.5 Multinomial Model; 2.2.3.6 Exponential Model; 2.2.3.7 Poisson Model; 2.2.3.8 Shift of a Laplace (Double Exponential) Law; 2.2.3.9 Shift of a Symmetric Density; 2.3 Unbiased Estimates, Bias, and Quadratic Risk; 2.3.1 Univariate Parameter; 2.3.2 Multivariate Case; 2.4 Asymptotic Properties; 2.4.1 Root-n Normality: Univariate Parameter; 2.4.2 Root-n Normality: Multivariate Parameter; 2.5 Some Geometric Properties of a Parametric Family
880 8 $6505-00/(S$a2.8 Maximum Likelihood and Other Estimation Methods2.8.1 Minimum Distance Estimation; 2.8.2 M-Estimation and Maximum Likelihood Estimation; 2.8.2.1 Least Squares Estimation; 2.8.2.2 LAD (Median) Estimation; 2.8.2.3 Maximum Likelihood Estimation; 2.9 Maximum Likelihood for Some Parametric Families; 2.9.1 Gaussian Shift; 2.9.2 Variance Estimation for the Normal Law; 2.9.3 Univariate Normal Distribution; 2.9.4 Uniform Distribution on [0,θ]; 2.9.5 Bernoulli or Binomial Model; 2.9.6 Multinomial Model; 2.9.7 Exponential Model; 2.9.8 Poisson Model; 2.9.9 Shift of a Laplace (Double Exponential) Law
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