Lecture notes:
Inference 1:
Lecture -1: Review of Linear Algebra
Lecture 0: Gaussian random vectors (From Prof. Iain Johnstone)
Lecture 2: Sufficient Statistics
Lecture 3: Convex functions and Blackwell-Rao
Lecture 4: Minimal sufficiency
Lecture 5: Complete sufficiency
Lecture 6: Exponential families and sufficiency
Lecture 7: Exponential families and maximum likelihood
Lecture 8: Unbiased estimators and completeness
Lecture 9: Fisher information and Cramer-Rao lower bound
Lecture 10r: Review of the linear algebra
Lecture 10: Fisher information matrix
Lecture 11: Inadmissibility of UMVU and ML
Lecture 12: Bayesisn estimation I
Lecture 13: Bayesian estimation II
Lecture 14: Bayesian estimation III
Lecture 15: Bayesian estimation IV
Lecture 16: Numeric integration
Lecture 17: Bayesian calculations
Lecture 18: Minimax definition
Lecture 19: Analytic functions
Lecture 20: Bayes and minimality
Lecture 21: Minimax framework IV
Lecture 22: Proof of minimax theorem
Inference 2:
Lecture 1: Convergence in distribution/probability
Lecture 2: Slutsky's theorem
Lecture 3: Continuous mapping theorem
Lecture 4: Method of moments
Lecture 5: Scaling notations (deterministic)
Lecture 6: Scaling notations (stochastic)
Lecture 6 clarification: differentiability
Lecture 7: Plug-in estimators and Delta method
Lecture 8: Delta method continued
Lecture 9: MLE (heuristic argument)
Lecture 10: Consistency of MLE
Lecture 11: Uniform weak law of large numbers
Lecture 12: Consistency of MLE continued
Lecture 13: Asymptotic normality of MLE
Lecture 14: Quadratic mean differentiability
Lecture 15: Quadratic mean differentiability and MLE
Lecture 16: M-estimatros and Robust estimation
Lecture 17: Hypothesis testing I
Lecture 18: Neyman-Pearson paradigm
Lecture 19: Uniformly most powerful tests
Lecture 20: Composite null (finite case)
Lecture 21: Composite null (uncountable)
Lecture 22: Composite null (uncountable II)
Lecture 23: Unbiased testing
Lecture 24: Likelihood ratio tests
Homeworks:
Inference 1:
Homework 1; Solution to HW1
Homework 2; Solution to HW2
Homework 3; Solution to HW3
Homework 4; Solution to HW4
Homework 5; Solution to HW5
Homework 6; Solution to HW6
Homework 7; Solution to HW7
Homework 8; Solution to HW8
Homework 9; Solution to HW9
Bayes Examples;
Homework 10; Solution to HW10
Homework 11; Solution to HW11
Inference 2:
Homework 1;
Homework 2; Solution to HW2
Homework 3; Solution to HW3
Homework 4; Solution to HW4
Homework 5; Solution to HW5
Homework 6; Solution to HW6
Homework 7; Solution to HW7
Homework 8; Solution to HW8
Homework 9; Solution to HW9
Homework 10; Solution to HW10
Homework 11; Solution to HW11
Exams:
Inference 1:
Midterm exam; Midterm solution; Histogram
Final Exam; Histogram; Final solutions
Inference 2:
Midterm exam;
Final exam;