Statistical Inference

  1. Point Estimation
    1. The Objective of Point Estimation
      1. Estimating Unknown Parameters
        1. Using Sample Data for Estimation
          1. Point Estimate vs True Parameter
          2. Desirable Properties of Point Estimators
            1. Unbiasedness
              1. Definition and Mathematical Expression
                1. Examples of Unbiased Estimators
                  1. Examples of Biased Estimators
                    1. Bias-Variance Tradeoff
                    2. Efficiency
                      1. Definition and Comparison of Estimators
                        1. Minimum Variance Unbiased Estimators
                          1. Relative Efficiency
                            1. Cramér-Rao Lower Bound
                            2. Consistency
                              1. Definition and Mathematical Expression
                                1. Weak Consistency
                                  1. Strong Consistency
                                    1. Relationship to Unbiasedness
                                    2. Sufficiency
                                      1. Definition of Sufficient Statistics
                                        1. Factorization Theorem
                                          1. Minimal Sufficient Statistics
                                            1. Completeness
                                          2. Methods for Finding Estimators
                                            1. Method of Moments
                                              1. Principle and Procedure
                                                1. Population Moments vs Sample Moments
                                                  1. Examples of MOM Estimators
                                                    1. Properties of MOM Estimators
                                                    2. Maximum Likelihood Estimation
                                                      1. The Likelihood Function
                                                        1. Definition and Construction
                                                          1. Likelihood vs Probability
                                                            1. Joint Likelihood for Independent Observations
                                                            2. Finding the Maximum Likelihood Estimator
                                                              1. Optimization Techniques
                                                                1. Log-Likelihood Function
                                                                  1. Score Function and Information
                                                                    1. Numerical Methods
                                                                    2. Properties of MLEs
                                                                      1. Consistency
                                                                        1. Asymptotic Normality
                                                                          1. Asymptotic Efficiency
                                                                            1. Invariance Property
                                                                          2. Least Squares Estimation
                                                                            1. Principle of Least Squares
                                                                              1. Ordinary Least Squares
                                                                                1. Properties of Least Squares Estimators
                                                                                2. Bayesian Estimation
                                                                                  1. Prior and Posterior Distributions
                                                                                    1. Bayes Estimators
                                                                                      1. Maximum A Posteriori Estimation

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                                                                                  2. Sampling and Sampling Distributions

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                                                                                  4. Interval Estimation and Confidence Intervals