Kernel Density Estimation: Bandwidth Selection and Curse of Dimensionality

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Page 3 of 4

Explores implicit generative models, covering topics like method of moments, kernel choice, and robustness of estimators.

Model Selection: Non-Nested Model Selection

Explores model selection, criteria, bias/variance tradeoff, and cross-validation methods.

Sampling Distributions: Estimators and Variance

Covers estimation of parameters, MSE, Fisher information, and the Rao-Blackwell Theorem.

Estimators: Consistency and Efficiency

Explores the criteria for good estimators, emphasizing consistency and efficiency in estimation.

Parametric Models

Explores statistical estimation, regression models, and model selection in parametric models.

Dimensionality Reduction: PCA and LDA

Covers dimensionality reduction techniques like PCA and LDA, clustering methods, density estimation, and data representation.

Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

Statistical Learning Models: Risk and Empirical Risk Minimization

Covers statistical learning models, risk minimization, and empirical risk minimization with examples of maximum-likelihood estimators.

Statistical Estimation: Gaussian Linear Model

Delves into statistical estimation, highlighting the Gaussian linear model and the limitations of ML estimators.

Spectral & Parametric Estimation: Time Series

Covers spectral estimation techniques like tapering and parametric estimation, emphasizing the importance of AR models and Whittle likelihood in time series analysis.