Lectures related to Sampling distribution

Sampling Distributions: Theory and Applications

Explores sampling distributions, estimators' properties, and statistical measures for data science applications.

Gauss-Markov Theorem: Optimal Estimation

Explores the Gauss-Markov Theorem and the optimality of Least Squares Estimators in the Gaussian Linear model.

Optimality and Asymptotics

Explores the optimality of the Least Squares Estimator and its large sample distribution.

Sampling Distributions: Understanding Ancillary Statistics

Explores ancillary statistics, sufficiency, and minimally sufficient statistics in sampling distributions.

Correlated and Uncorrelated Sampling

Explains correlated and uncorrelated sampling for generating random variables with given weight functions.

Statistical Analysis: Data Exploration and Inference

Covers statistical analysis, emphasizing data exploration and inference to quantify uncertainty and draw conclusions.

Statistics & Experimental Design

Explores conditional probability, Framingham studies, effect size, t-test, and sampling error in statistics.

Errors in Correlated Sampling

Explains errors in correlated and uncorrelated sampling, correlation function, time, and blocking analysis.

Sampling Distributions: Theory and Applications

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

Entropy and Sampling Theory

Explores entropy, exponential family, sampling theory, and statistical inference from samples.

Sampling Theory: Statistics and Inference

Covers sampling theory, statistics, and inference, focusing on the sampling distribution of statistics.

Sampling Theory: Statistics for Mathematicians

Covers the theory of sampling, focusing on statistics for mathematicians.

Sampling Distributions: Estimators and Variance

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

Distribution Theory of Least Squares

Explores the distribution theory of least squares estimators in a Gaussian linear model, focusing on precision and confidence intervals construction.

Central Limit Theorem: Proof

Presents the proof of the Central Limit Theorem using Lindeberg's principle.

Statistical Models and Parameter Estimation

Explores statistical models, parameter estimation, and sampling distributions in probability and statistics.

Sufficient Statistics: Understanding Data Compression

Explores sufficient statistics, data compression, and their role in statistical inference, with examples like Bernoulli Trials and exponential families.

Sampling Distributions: Estimation

Explores sampling distributions, estimation methods, and consistency in parameter estimation.

Statistical Models: Sampling and Hypothesis Testing

Explores statistical models, sampling distributions, and hypothesis testing using real-world examples.

Errors in Sampling: Correlation and Time Analysis

Explores errors in sampling, correlation functions, time analysis, and blocking techniques.