Basics of modern mathematical statistics. ([2014])
- Record Type:
- Book
- Title:
- Basics of modern mathematical statistics. ([2014])
- Main Title:
- Basics of modern mathematical statistics
- Further Information:
- Note: Vladimir Spokoiny, Thorsten Dickhaus.
- Authors:
- Spokoiny, V. G
Dickhaus, Thorsten - Contents:
- Intro; 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 2.5.1 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 2.10 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 CanonicalIntro; 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 2.5.1 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 2.10 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 … (more)
- Publisher Details:
- Berlin : Springer
- Publication Date:
- 2014
- Copyright Date:
- 2015
- Extent:
- 1 online resource
- Subjects:
- 519.5
Mathematical statistics
Mathematics
Statistics as Topic
Mathematical statistics
Electronic books - Languages:
- English
- ISBNs:
- 9783642399091
3642399096 - Related ISBNs:
- 9783642399084
- Notes:
- Note: Includes bibliographical references.
Note: Print version record. - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.397159
- Ingest File:
- 02_424.xml