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William Mitchell
William Mitchell

Statistics and Econometric Models Volume 1 PDF: An Introduction to General Concepts and Methods

Statistics and Econometric Models Volume 1 PDF: A Comprehensive Guide

If you are looking for a comprehensive guide on statistics and econometric models, you might want to check out Statistics and Econometric Models Volume 1 by Christian Gourieroux and Alain Monfort. This book provides an introduction to general concepts and methods in statistics and econometrics, and covers topics such as estimation, prediction, and algorithms. In this article, we will give you an overview of the book and its contents, and show you how you can access it online.

Statistics And Econometric Models Volume 1 Pdf

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Chapter 1: Models

The first chapter of the book introduces the concept of models and their usefulness in statistics and econometrics. A model is a simplified representation of a complex reality, which allows us to understand, explain, and predict phenomena of interest. The authors discuss the main types of models in statistics and econometrics, such as deterministic models, stochastic models, parametric models, nonparametric models, linear models, nonlinear models, dynamic models, and static models. They also present the criteria for evaluating models, such as consistency, efficiency, robustness, parsimony, and goodness-of-fit.

Chapter 2: Statistical Problems and Decision Theory

The second chapter of the book formulates the statistical problems that arise from using models to analyze data. A statistical problem is a situation where we have to make a decision based on incomplete or uncertain information. The authors introduce the concept of decision rules, which are functions that map the available information to a set of possible actions. They also explain the main concepts and principles of decision theory, such as loss functions, risk functions, admissibility, minimaxity, Bayes rules, and dominance.

Chapter 3: Statistical Information: Classical Approach

The third chapter of the book measures the statistical information contained in the data and the model. Statistical information is the amount of knowledge or uncertainty that we have about the parameters or variables of interest. The authors use the classical approach to statistics, which is based on the notion of probability as a measure of frequency or likelihood. They introduce the concepts of sufficiency, ancillarity, completeness, and identification, which are properties that characterize the quality and quantity of statistical information. They also show how these concepts affect estimation and testing procedures.

Chapter 4: Bayesian Interpretations of Sufficiency, Ancillarity, and Identification

The fourth chapter of the book reinterprets the concepts of sufficiency, ancillarity, and identification from a Bayesian perspective. The Bayesian approach to statistics is based on the notion of probability as a measure of belief or plausibility. The authors show how sufficiency, ancillarity, and identification can be defined in terms of prior information and posterior distributions. They also compare and contrast the Bayesian approach with the classical approach.

Chapter 5: Elements of Estimation Theory

The fifth chapter of the book introduces the theory of estimation, which is one of the main goals of statistics and econometrics. Estimation is the process of inferring unknown parameters or variables from observed data. The authors define estimators as functions that map data to estimates. They also discuss the properties of estimators, such as unbiasedness, consistency, efficiency, asymptotic normality, and confidence intervals.

Chapter 6: Unbiased Estimation

The sixth chapter of the book focuses on unbiased estimation, which is one of the most desirable properties of estimators. An estimator is unbiased if its expected value equals the true value of the parameter or variable being estimated. The authors present the methods for obtaining unbiased estimators, such as method of moments, least squares method, instrumental variables method, generalized least squares method, maximum likelihood method, and best linear unbiased estimator method. They also discuss the limitations and trade-offs of unbiased estimation, such as variance-bias trade-off, existence-uniqueness trade-off, and efficiency-robustness trade-off.

Chapter 7: Maximum Likelihood Estimation

The seventh chapter of the book covers maximum likelihood estimation (MLE), which is one of the most popular and powerful methods for estimation. MLE is based on maximizing a function called likelihood function, which measures how likely or plausible a given parameter value is given the observed data. The authors explain how MLE works and what are its advantages and disadvantages. They also present some extensions and applications of MLE, such as constrained MLE, profile MLE, quasi-MLE, and composite MLE.

Chapter 8: M-Estimation

The eighth chapter of the book introduces M-estimation, which is a generalization of MLE that allows for more flexibility and robustness. M-estimation is based on minimizing a function called criterion function, which can be derived from different sources such as moment conditions, distance measures, or loss functions. The authors provide some examples and properties of M-estimators, such as generalized method of moments (G 71b2f0854b


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