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**Category:**Interesting articles (continued)**Category:**INTRODUCTION TO STATISTICS AND ECONOMETRICS- INTRODUCTION TO STATISTICS AND ECONOMETRICS
- WHAT IS PROBABILITY?
- WHAT IS STATISTICS?
- PROBABILITY
- COUNTING TECHNIQUES
- Permutations and Combinations
- CONDITIONAL PROBABILITY AND INDEPENDENCE
- Bayes' Theorem
- Statistical Independence
- PROBABILITY CALCULATIONS
- RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
- DISCRETE RANDOM VARIABLES
- Bivariate Random Variables
- Multivariate Random Variables
- UNIVARIATE CONTINUOUS RANDOM VARIABLES
- Conditional Density Function
- BIVARIATE CONTINUOUS RANDOM VARIABLES
- Marginal Density
- Conditional Density
- Independence
- DISTRIBUTION FUNCTION
- CHANGE OF VARIABLES
- JOINT DISTRIBUTION OF DISCRETE AND CONTINUOUS RANDOM VARIABLES
- MOMENTS
- HIGHER MOMENTS
- COVARIANCE AND CORRELATION
- CONDITIONAL MEAN AND VARIANCE
- BINOMIAL AND NORMAL RANDOM VARIABLES
- NORMAL RANDOM VARIABLES
- MULTIVARIATE NORMAL RANDOM VARIABLES
- MODES OF CONVERGENCE
- LAWS OF LARGE NUMBERS AND CENTRAL LIMIT THEOREMS
- NORMAL APPROXIMATION OF BINOMIAL
- EXAMPLES
- WHAT IS AN ESTIMATOR?
- Sample Moments
- Estimators in General
- Nonparametric Estimation
- Various Measures of Closeness
- Strategies for Choosing an Estimator
- Best Linear Unbiased Estimator
- Asymptotic Properties
- MAXIMUM LIKELIHOOD ESTIMATOR: DEFINITION AND COMPUTATION
- Continuous Sample
- 7.4 MAXIMUM LIKELIHOOD ESTIMATOR: PROPERTIES
- Cramer-Rao Lower Bound
- Asymptotic Normality
- CONFIDENCE INTERVALS
- BAYESIAN METHOD
- TYPE I AND TYPE II ERRORS
- NEYMAN-PEARSON LEMMA
- SIMPLE AGAINST COMPOSITE
- COMPOSITE AGAINST COMPOSITE
- EXAMPLES OF HYPOTHESIS TESTS
- TESTING ABOUT A VECTOR PARAMETER
- Variance-Covariance Matrix Assumed Known
- BIVARIATE REGRESSION MODEL
- LEAST SQUARES ESTIMATORS
- Properties of a. and j3
- Estimation of a2
- Asymptotic Properties of Least Squares Estimators
- Maximum Likelihood Estimators
- Prediction
- TESTS OF HYPOTHESES
- Tests for Structural Change
- ELEMENTS OF MATRIX ANALYSIS
- DEFINITION OF BASIC TERMS
- MATRIX OPERATIONS
- DETERMINANTS AND INVERSES
- SIMULTANEOUS LINEAR EQUATIONS
- PROPERTIES OF THE SYMMETRIC MATRIX
- MULTIPLE REGRESSION MODEL
- Student's t Test
- The F Test
- SELECTION OF REGRESSORS
- GENERALIZED LEAST SQUARES
- Known Variance-Covariance Matrix
- Heteroscedasticity
- Serial Correlation
- Error Components Model
- TIME SERIES REGRESSION
- SIMULTANEOUS EQUATIONS MODEL
- NONLINEAR REGRESSION MODEL
- QUALITATIVE RESPONSE MODEL
- Binary Model
- Multinomial Model
- CENSORED OR TRUNCATED REGRESSION MODEL (TOBIT MODEL)
- DURATION MODEL
- APPENDIX: DISTRIBUTION THEORY

**Category:**Introduction to the Mathematical and Statistical Foundations of Econometrics- Introduction to the Mathematical and Statistical Foundations of Econometrics
- Probability and Measure
- Binomial Numbers
- Sample Space
- Probability Measure
- Quality Control
- Quality Control in Practice
- Sampling with Replacement
- Why Do We Need Sigma-Algebras of Events?
- Properties of Algebras and Sigma-Algebras
- Borel Sets
- Outer Measure
- Lebesgue Integral
- Random Variables and Their Distributions
- Density Func tions
- Conditional Probability, Bayes’ Rule, and Independence
- Bayes’ Rule
- Sets in Euclidean Spaces
- B. Extension of an Outer Measure to a Probability Measure
- Borel Measurability, Integration, and Mathematical Expectations
- Borel Measurability
- Mathematical Expectation
- Liapounov’s Inequality
- Expectations of Products of Independent Random Variables
- Moment-Generating Functions and Characteristic Functions
- Conditional Expectations
- Properties of Conditional Expectations
- Conditional Probability Measures and Conditional Independence
- Conditioning on Increasing Sigma-Algebras
- Conditional Expectations as the Best Forecast Schemes
- Distributions and Transformations
- The Binomial Distribution A random variable X has a binomial distribution if
- The Poisson Distribution
- Transformations of Discrete Random Variables and Vectors
- Transformations of Absolutely Continuous Random Variables
- Transformations of Absolutely Continuous Random Vectors 4.4.1. The Linear Case
- The Nonlinear Case
- The Normal Distribution
- Distributions Related to the Standard Normal Distribution
- The Student’s t Distribution
- The Standard Cauchy Distribution
- The Uniform Distribution and Its Relation to the Standard Normal Distribution
- The Multivariate Normal Distribution and Its Application to Statistical Inference
- The Multivariate Normal Distribution
- Follows now from Theorem 5.2. Q. E. D
- Conditional Distributions of Multivariate Normal Random Variables
- Independence of Linear and Quadratic Transformations of Multivariate Normal Random Variables
- Distributions of Quadratic Forms of Multivariate Normal Random Variables
- Applications to Statistical Inference under Normality
- Confidence Intervals
- Testing Parameter Hypotheses
- Applications to Regression Analysis
- Least-Squares Estimation Observe that
- Hypotheses Testing
- Modes of Convergence
- Convergence in Probability and the Weak Law of Large Numbers
- The Uniform Law of Large Numbers and Its Applications
- Applications of the Uniform Weak Law of Large Numbers
- Generalized Slutsky’s Theorem
- Convergence in Distribution
- Convergence of Characteristic Functions
- The Central Limit Theorem
- Asymptotic Normality of M-Estimators
- B.2. Slutsky’s Theorem
- Convergence of Characteristic Functions and Distributions
- Dependent Laws of Large Numbers and Central Limit Theorems
- Weak Laws of Large Numbers for Stationary Processes
- Mixing Conditions
- Uniform Weak Laws of Large Numbers
- Dependent Central Limit Theorems
- A Generic Central Limit Theorem
- A.2. A Hilbert Space of Random Variables
- A.5. Proof of the Wold Decomposition
- Maximum Likelihood Theory
- Likelihood Functions
- Linear Regression with Normal Errors
- The Tobit Model
- Asymptotic Properties of ML Estimators
- First - and Second-Order Conditions
- Generic Conditions for Consistency and Asymptotic Normality
- Asymptotic Efficiency of the ML Estimator
- Testing Parameter Restrictions
- The Lagrange Multiplier Test
- Selecting a Test
- Appendix I - Review of Linear Algebra
- The Inverse and Transpose of a Matrix
- Elementary Matrices and Permutation Matrices
- Gaussian Elimination of a Square Matrix and the Gauss-Jordan Iteration for Inverting a Matrix
- The Gauss-Jordan Iteration for Inverting a Matrix
- Gaussian Elimination of a Nonsquare Matrix
- Subspaces Spanned by the Columns and Rows of a Matrix
- Projections, Projection Matrices, and Idempotent Matrices
- Inner Product, Orthogonal Bases, and Orthogonal Matrices
- Determinants of Block-Triangular Matrices
- Inverse of a Matrix in Terms of Cofactors
- Eigenvalues and Eigenvectors
- Eigenvectors
- Eigenvalues and Eigenvectors of Symmetric Matrices
- Positive Definite and Semidefinite Matrices
- Generalized Eigenvalues and Eigenvectors
- Appendix II - Miscellaneous Mathematics
- Supremum and Infimum
- Limsup and Liminf
- Continuity of Concave and Convex Functions
- Uniform Continuity
- The Mean Value Theorem
- Taylor’s Theorem
- Appendix III - A Brief Review of Complex Analysis
- The Complex Exponential Function
- The Complex Logarithm
- Series Expansion of the Complex Logarithm
- Appendix IV - Tables of Critical Values

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