Statistical Computing

  1. Statistical Model Implementation
    1. Linear Models
      1. Simple Linear Regression
        1. Model Specification
          1. Parameter Estimation
            1. Residual Analysis
              1. Diagnostic Plots
              2. Multiple Linear Regression
                1. Matrix Formulation
                  1. QR Decomposition Approach
                    1. SVD Approach
                      1. Collinearity Issues
                      2. Generalized Linear Models
                        1. Exponential Family Distributions
                          1. Iteratively Reweighted Least Squares
                            1. Deviance and Model Comparison
                            2. Model Diagnostics
                              1. Residual Analysis
                                1. Influence Measures
                                  1. Outlier Detection
                                    1. Model Validation
                                  2. Non-linear and Flexible Models
                                    1. Non-linear Regression
                                      1. Non-linear Least Squares
                                        1. Gauss-Newton Algorithm
                                          1. Levenberg-Marquardt Algorithm
                                            1. Parameter Initialization
                                            2. Generalized Additive Models
                                              1. Smoothing Splines
                                                1. Local Regression (LOESS)
                                                  1. Penalized Regression Splines
                                                    1. Model Selection and Smoothing Parameter Estimation
                                                    2. Mixed-Effects Models
                                                      1. Random Effects Specification
                                                        1. REML Estimation
                                                          1. Nested and Crossed Random Effects
                                                            1. Model Comparison
                                                            2. Survival Analysis Models
                                                              1. Kaplan-Meier Estimation
                                                                1. Cox Proportional Hazards Model
                                                                  1. Parametric Survival Models
                                                                2. Machine Learning Algorithms
                                                                  1. Tree-Based Methods
                                                                    1. Decision Trees
                                                                      1. Splitting Criteria
                                                                        1. Pruning Methods
                                                                          1. Handling Missing Values
                                                                          2. Random Forests
                                                                            1. Bootstrap Aggregating
                                                                              1. Variable Importance
                                                                                1. Out-of-Bag Error
                                                                                2. Gradient Boosting
                                                                                  1. AdaBoost
                                                                                    1. Gradient Boosting Machines
                                                                                      1. XGBoost Implementation
                                                                                    2. Support Vector Machines
                                                                                      1. Linear SVM
                                                                                        1. Kernel Methods
                                                                                          1. Polynomial Kernels
                                                                                            1. RBF Kernels
                                                                                              1. Custom Kernels
                                                                                              2. Multi-class Classification
                                                                                              3. Neural Networks
                                                                                                1. Perceptron
                                                                                                  1. Multi-layer Perceptrons
                                                                                                    1. Backpropagation Algorithm
                                                                                                      1. Regularization Techniques
                                                                                                      2. Clustering Algorithms
                                                                                                        1. K-Means Clustering
                                                                                                          1. Hierarchical Clustering
                                                                                                            1. Density-Based Clustering
                                                                                                              1. Model-Based Clustering
                                                                                                              2. Dimensionality Reduction
                                                                                                                1. Principal Component Analysis
                                                                                                                  1. Independent Component Analysis
                                                                                                                    1. t-SNE
                                                                                                                      1. UMAP
                                                                                                                    2. Time Series Models
                                                                                                                      1. ARIMA Models
                                                                                                                        1. Autoregressive Models
                                                                                                                          1. Moving Average Models
                                                                                                                            1. Integrated Models
                                                                                                                              1. Model Identification and Estimation
                                                                                                                              2. State Space Models
                                                                                                                                1. Kalman Filter
                                                                                                                                  1. Particle Filter
                                                                                                                                    1. Hidden Markov Models
                                                                                                                                    2. Volatility Models
                                                                                                                                      1. ARCH Models
                                                                                                                                        1. GARCH Models

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                                                                                                                                    6. Advanced Computational Methods

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                                                                                                                                    8. Visualization and Communication