Lectures related to Statistical Estimators

Explores bias, variance, unbiased estimators, and confidence intervals in statistical estimation.

Covers the concept of mean-square-error inference and optimal estimators for inference problems using different design criteria.

Basic Principles of Point Estimation

Explores the Method of Moments, Bias-Variance tradeoff, Consistency, Plug-In Principle, and Likelihood Principle in point estimation.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Estimators and Bias

Explores estimators, bias, and efficiency in statistics, emphasizing the trade-off between bias and variability.

Intro to Quantum Sensing: Parameter Estimation and Fisher Information

Introduces Fisher Information for parameter estimation based on collected data.

Optimality in Decision Theory: Unbiased Estimation

Explores optimality in decision theory and unbiased estimation, emphasizing sufficiency, completeness, and lower bounds for risk.

Statistical Models and Parameter Estimation

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

Law of Large Numbers: Strong Convergence

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

Sampling Distributions: Estimators and Variance

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

Confidence Intervals: Definition and Estimation

Explains confidence intervals, parameter estimation methods, and the central limit theorem in statistical inference.

Statistical Theory: Maximum Likelihood Estimation

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

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Sampling Distributions: Theory and Applications

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

Elements of Statistics: Probability, Distributions, and Estimation

Covers probability theory, distributions, and estimation in statistics, emphasizing accuracy, precision, and resolution of measurements.

Probabilistic Models for Linear Regression

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

Estimators: Consistency and Efficiency

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

Statistical Estimation

Explores statistical estimation, comparing estimators based on mean and variance, and delving into mean squared error and Cramér-Rao bound.

Point Estimation in Statistics

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

Maximum Likelihood Estimation

Explores Maximum Likelihood Estimation, covering assumptions, properties, distribution, shrinkage estimation, and loss functions.