Sampling Theory

  1. Advanced Estimation Techniques
    1. Ratio Estimation
      1. Ratio Estimator Definition
        1. Conditions for Effective Use
          1. Bias Properties
            1. Approximate Unbiasedness
              1. Bias Magnitude
              2. Mean Squared Error
                1. MSE Components
                  1. Efficiency Comparisons
                  2. Applications and Examples
                    1. Limitations and Assumptions
                    2. Regression Estimation
                      1. Linear Regression Estimator
                        1. Auxiliary Variable Requirements
                          1. Assumptions and Conditions
                            1. Bias and Variance Properties
                              1. Comparison with Ratio Estimation
                                1. Efficiency Gains
                                  1. Multiple Regression Extensions
                                  2. Difference Estimation
                                    1. Difference Estimator Definition
                                      1. Appropriate Use Cases
                                        1. Bias Properties
                                          1. Variance Characteristics
                                            1. Comparison with Other Methods
                                            2. Combined Ratio and Regression Estimation
                                              1. Hybrid Approaches
                                                1. Optimal Combinations
                                                  1. Practical Applications

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                                                4. Estimation from Samples

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                                                6. Sample Size Determination