Lectures related to Asymptotic distribution

Implicit Generative Models

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

Likelihood Ratio Test: Hypothesis Testing

Covers the Likelihood Ratio Test and hypothesis testing methods using Maximum Likelihood Estimators.

Limiting Distribution and Ergodic Theorem

Explores limiting distribution in Markov chains and the implications of ergodicity and aperiodicity on stationary distributions.

Generalized Linear Models: GLMs for Non-Gaussian Data

Explores Generalized Linear Models for non-Gaussian data, covering interpretation of natural link function, MLE asymptotic normality, deviance measures, residuals, and logistic regression.

Feynman Rules I: Asymptotic Statistic and Instantons

Covers the Feynman Rules, Asymptotic Statistics, Normal Ordering, and Instantons.

Generalized Linear Models: Theory and Applications

Covers the theory and applications of Generalized Linear Models, including MLE, measures of fit, shrinkage, and special examples.

Debiased Whittle Likelihood: Time Series and Spatial Data

Explores the Debiased Whittle likelihood for time series and spatial data, focusing on fitting spectral density to the periodogram for better predictions and parameter estimation.

Maximum Likelihood Estimation: Properties and Applications

Explores the properties and challenges of Maximum Likelihood Estimators.

Extreme Value Theory: Limiting Distributions and Applications

Covers Extreme Value Theory, GEV distributions, GPD, and threshold exceedances.

Weighted Least Squares Estimation: IRLS Algorithm

Explores the IRLS algorithm for weighted least squares estimation in GLM.

Estimation, Shrinkage and Penalization

Covers estimation, shrinkage, and penalization in statistics for data science, emphasizing the importance of balancing bias and variance in model estimation.

Sampling Distributions: Theory and Applications

Explores sampling theory, limiting distributions, and estimation for statistical analysis.

Confidence Intervals: Gaussian Estimation

Explores confidence intervals, Gaussian estimation, Cramér-Rao inequality, and Maximum Likelihood Estimators.

Point Estimation in Statistics

Explores point estimation in statistics, discussing bias, variance, mean squared error, and consistency of estimators.

Central Limit Theorem: Multivariate Delta Method

Explores the Central Limit Theorem, Slutsky's Theorem, and the Multivariate Delta Method in probability and distribution convergence.

Gaussian Linear Regression: Assumptions and Residuals

Explores the assumptions and checking methods for Gaussian linear regression models using residuals and graphical plots.

Fisher Information, Cramér-Rao Inequality, MLE

Explains Fisher information, Cramér-Rao inequality, and MLE properties, including invariance and asymptotics.

Maximum Likelihood Estimation Log in to Mediaspace to watch this video

Delves into maximum likelihood estimators, their properties, and asymptotic behavior, emphasizing consistency and asymptotic normality.

Likelihood Ratio Tests: Optimality and Extensions Log in to Mediaspace to watch this video

Covers Likelihood Ratio Tests, their optimality, and extensions in hypothesis testing, including Wilks' Theorem and the relationship with Confidence Intervals.

Statistical Theory: Maximum Likelihood Estimation Log in to Mediaspace to watch this video

Explores the consistency and asymptotic properties of the Maximum Likelihood Estimator, including challenges in proving its consistency and constructing MLE-like estimators.