Fundamental statistical inference a computational approach 1st Edition by Marc Paolella 1119417880 9781119417880

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ISBN-10 :  1119417880 

ISBN-13 :  9781119417880

Author:  Marc S. Paolella 

A hands-on approach to statistical inference that addresses the latest developments in this ever-growing field This clear and accessible book for beginning graduate students offers a practical and detailed approach to the field of statistical inference, providing complete derivations of results, discussions, and MATLAB programs for computation. It emphasizes details of the relevance of the material, intuition, and discussions with a view towards very modern statistical inference. In addition to classic subjects associated with mathematical statistics, topics include an intuitive presentation of the (single and double) bootstrap for confidence interval calculations, shrinkage estimation, tail (maximal moment) estimation, and a variety of methods of point estimation besides maximum likelihood, including use of characteristic functions, and indirect inference. Practical examples of all methods are given. Estimation issues associated with the discrete mixtures of normal distribution, and their solutions, are developed in detail. Much emphasis throughout is on non-Gaussian distributions, including details on working with the stable Paretian distribution and fast calculation of the noncentral Student’s t. An entire chapter is dedicated to optimization, including development of Hessian-based methods, as well as heuristic/genetic algorithms that do not require continuity, with MATLAB codes provided. The book includes both theory and nontechnical discussions, along with a substantial reference to the literature, with an emphasis on alternative, more modern approaches. The recent literature on the misuse of hypothesis testing and p-values for model selection is discussed, and emphasis is given to alternative model selection methods, though hypothesis testing of distributional assumptions is covered in detail, notably for the normal distribution.  Presented in three parts—Essential Concepts in Statistics; Further Fundamental Concepts in Statistics; and Additional Topics—Fundamental Statistical Inference: A Computational Approach offers comprehensive chapters on: Introducing Point and Interval Estimation; Goodness of Fit and Hypothesis Testing; Likelihood; Numerical Optimization; Methods of Point Estimation; Q-Q Plots and Distribution Testing; Unbiased Point Estimation and Bias Reduction; Analytic Interval Estimation; Inference in a Heavy-Tailed Context; The Method of Indirect Inference; and, as an appendix, A Review of Fundamental Concepts in Probability Theory, the latter to keep the book self-contained, and giving material on some advanced subjects such as saddlepoint approximations, expected shortfall in finance, calculation with the stable Paretian distribution, and convergence theorems and proofs. 

Fundamental statistical inference a computational approach 1st Table of contents:

Part I: Essential Concepts in Statistics
Chapter 1: Introducing Point and Interval Estimation
1.1 Point Estimation
1.2 Interval Estimation via Simulation
1.3 Interval Estimation via the Bootstrap
1.4 Bootstrap Confidence Intervals in the Geometric Model
1.5 Problems
Chapter 2: Goodness of Fit and Hypothesis Testing
2.1 Empirical Cumulative Distribution Function
2.2 Comparing Parametric and Nonparametric Methods
2.3 Kolmogorov–Smirnov Distance and Hypothesis Testing
2.4 Testing Normality with KD and AD
2.5 Testing Normality with and
2.6 Testing the Stable Paretian Distributional Assumption: First Attempt
2.7 Two-Sample Kolmogorov Test
2.8 More on (Moron?) Hypothesis Testing
2.9 Problems
Chapter 3: Likelihood
3.1 Introduction
3.2 Cramér–Rao Lower Bound
3.3 Model Selection
3.4 Problems
Chapter 4: Numerical Optimization
4.1 Root Finding
4.2 Approximating the Distribution of the Maximum Likelihood Estimator
4.3 General Numerical Likelihood Maximization
4.4 Evolutionary Algorithms
4.5 Problems
Chapter 5: Methods of Point Estimation
5.1 Univariate Mixed Normal Distribution
5.2 Alternative Point Estimation Methodologies
5.3 Comparison of Methods
5.4 A Primer on Shrinkage Estimation
5.5 Problems
Part II: Further Fundamental Concepts in Statistics
Chapter 6: Q-Q Plots and Distribution Testing
6.1 P-P Plots and Q-Q Plots
6.2 Null Bands
6.3 Q-Q Test
6.4 Further P-P and Q-Q Type Plots
6.5 Further Tests for Composite Normality
6.6 Combining Tests and Power Envelopes
6.7 Details of a Failed Attempt
6.8 Problems
Chapter 7: Unbiased Point Estimation and Bias Reduction
7.1 Sufficiency
7.2 Completeness and the Uniformly Minimum Variance Unbiased Estimator
7.3 An Example with i.i.d. Geometric Data
7.4 Methods of Bias Reduction
7.5 Problems
Chapter 8: Analytic Interval Estimation
8.1 Definitions
8.2 Pivotal Method
8.3 Intervals Associated with Normal Samples
8.4 Cumulative Distribution Function Inversion
8.5 Application of the Nonparametric Bootstrap
Problems
Part III: Additional Topics
Chapter 9: Inference in a Heavy-Tailed Context
9.1 Estimating the Maximally Existing Moment
9.2 A Primer on Tail Estimation
9.3 Noncentral Student’s t Estimation
9.4 Asymmetric Stable Paretian Estimation
9.5 Testing the Stable Paretian Distribution
Chapter 10: The Method of Indirect Inference
10.1 Introduction
10.2 Application to the Laplace Distribution
10.3 Application to Randomized Response
10.4 Application to the Stable Paretian Distribution

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