Asymptotic statistical inference : a basic course using R

Asymptotic statistical inference : a basic course using R / Shailaja Deshmukh, Madhuri Kulkarni.

The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable no...

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Bibliographic Details
Main Author: Deshmukh, Shailaja
Other Authors: Kulkarni, Madhuri
Format: eBook
Language:English
Published: Singapore : Springer, 2021.
Subjects:
Mathematical statistics > Asymptotic theory.
Estadística matemática > Teoría asintótica
Mathematical statistics > Asymptotic theory
Estadística matemàtica.
Llibres electrònics.
Online Access:Click for online access
Table of Contents:
  • Intro
  • Preface
  • Contents
  • About the Authors
  • List of Figures
  • List of Tables
  • 1 Introduction
  • 1.1 Introduction
  • 1.2 Basics of Parametric Inference
  • 1.3 Basics of Asymptotic Inference
  • 1.4 Introduction to R Software and Language
  • 2 Consistency of an Estimator
  • 2.1 Introduction
  • 2.2 Consistency: Real Parameter Setup
  • 2.3 Strong Consistency
  • 2.4 Uniform Weak and Strong Consistency
  • 2.5 Consistency: Vector Parameter Setup
  • 2.6 Performance of a Consistent Estimator
  • 2.7 Verification of Consistency Using R
  • 2.8 Conceptual Exercises
  • 2.9 Computational Exercises
  • 3 Consistent and Asymptotically Normal Estimators
  • 3.1 Introduction
  • 3.2 CAN Estimator: Real Parameter Setup
  • 3.3 CAN Estimator: Vector Parameter Setup
  • 3.4 Verification of CAN Property Using R
  • 3.5 Conceptual Exercises
  • 3.6 Computational Exercises
  • 4 CAN Estimators in Exponential and Cramér Families
  • 4.1 Introduction
  • 4.2 Exponential Family
  • 4.3 Cramér Family
  • 4.4 Iterative Procedures
  • 4.5 Maximum Likelihood Estimation Using R
  • 4.6 Conceptual Exercises
  • 4.7 Computational Exercises
  • 5 Large Sample Test Procedures
  • 5.1 Introduction
  • 5.2 Likelihood Ratio Test Procedure
  • 5.3 Large Sample Tests Using R
  • 5.4 Conceptual Exercises
  • 5.5 Computational Exercises
  • 6 Goodness of Fit Test and Tests for Contingency Tables
  • 6.1 Introduction
  • 6.2 Multinomial Distribution and Associated Tests
  • 6.3 Goodness of Fit Test
  • 6.4 Score Test and Wald's Test
  • 6.5 Tests for Contingency Tables
  • 6.6 Consistency of a Test Procedure
  • 6.7 Large Sample Tests Using R
  • 6.8 Conceptual Exercises
  • 6.9 Computational Exercises
  • 7 Solutions to Conceptual Exercises
  • 7.1 Chapter 2
  • 7.2 Chapter 3
  • 7.3 Chapter 4
  • 7.4 Chapter 5
  • 7.5 Chapter 6
  • 7.6 Multiple Choice Questions
  • 7.6.1 Chapter 2: Consistency of an Estimator
  • 7.6.2 Chapter 3: Consistent and Asymptotically Normal Estimators
  • 7.6.3 Chapter 4: CAN Estimators in Exponential and Cramér Families
  • 7.6.4 Chapter 5: Large Sample Test Procedures
  • 7.6.5 Chapter 6: Goodness of Fit Test and Tests for Contingency Tables
  • Appendix *-1.6pcIndex
  • Index

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