Course Information COMP 348 Principles of Programming Languages Instructor and Coordinator: Method of Contact: Email: Schedule: Lecture (Section U): Mon-Wed Tutorials UA, UB: Mon Tutorials UC, UE: Wed Tutorials UD: Fri Lecture (Section DD): Wed Tutorials DDDA, DDDB, DDDC: Tue Tutorials DDDD: Thu Office Hours: During class hours via ZOOM COMP 348 Principles of Programming […]
ECONOMETRICS I ECON GR5411 Lecture 22 – Panel Data I by Seyhan Erden Columbia University MA in Economics Hypothesis Testing: 𝐻”: 𝑐𝜃=0 These three tests are asymptotically equivalent under 𝐻” (however they behave differently in finite samples) 1. Likelihood ratio test: if the restriction is valid, then imposing it should not cause a large reduction
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Numerical Methods & Scientific Computing: lecture notes Data fitting Week 9: aim to cover Nonlinear least squares, steepest descent, Gauss-Newton (Lecture 17) QR factorization; Nonlinear model fitting (Lab 9) Levenberg-Marquardt algorithm (as trust region method) (Lecture 18) Numerical Methods & Scientific Computing: lecture notes Data fitting Fitting nonlinear models Recall, we could fit linear models
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Numerical Methods & Scientific Computing: lecture notes Stochastic simulation Statistical errors Week 4: aim to cover Monte Carlo integration, floating point numbers, roundo↵ error (Lecture 7) Confidence intervals, MC integration, roundo↵ error (Lab 4) Error propagation (Lecture 8) Numerical Methods & Scientific Computing: lecture notes Stochastic simulation Statistical errors Monte Carlo integration It is frequently
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Columbia University MA in Economics GR 5411 Econometrics I Seyhan Erden Midterm Exam (please specify the page number of each question when you are submitting your problem set to Gradescope) ___________________________________________________________________ Instructions: This exam has three questions and an academic integrity statement that you have to “sign”. Go to Courseworks Quizzes, start the exam there
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Numerical Methods & Scientific Computing: lecture notes Root-finding Week 6: aim to cover Numerical linear algebra: Gauss Elimination with Partial Pivoting (GEPP), operations count (Lecture 11) Newton’s method, 2D arrays (matrices) in MATLAB (Lab 6) LU factorization, special matrices (Lecture 12) Numerical Methods & Scientific Computing: lecture notes Linear Systems Trefethen’s Maxims In principle, the
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Numerical Methods & Scientific Computing: lecture notes Root-finding Newton’s method slope = f’(xn) y xn+1 y = f(x) based on slope of function xn x Numerical Methods & Scientific Computing: lecture notes Root-finding Derivation Taylor series around xn: f(xn+1)⇡f(xn)+f0(xn)(xn+1 xn)=0 which gives Newton-Raphson iteration: xn+1 = xn f (xn) . f0(xn) Again, a first order
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ECONOMETRICS I ECON GR5411 Lecture 3 – More on Probability Distribution and Large Sample Distribution Theory by Seyhan Erden Columbia University MA in Economics Joint and Marginal Probability Functions: If 𝑋 and 𝑌 has discrete distributions, the function 𝑓 𝑥, 𝑦 = Pr(𝑋 = 𝑥, 𝑌 = 𝑦) is called the joint probability distribution of
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Contents Answers to Exercises: week 1. Exercise set 1 Exercise Set 2 Exercise Set 3 Exercise Set 4 More Answers to Exercises: week 1. Exercise set 1 ans = 0.6667 ans = 8 ans = 1.2599 ans = 1.5850 ans = -0.1397 ans = 9.1545 – 4.1689i ans = 0.7071 – 0.7071i part b need
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ECONOMETRICS I ECON GR5411 Lectures 21 – MLE by Seyhan Erden Columbia University MA in Economics Maximum Likelihood Estimation: Probability density function (pdf) of a RV, 𝑦, conditioned on a set of parameters, 𝜃, is denoted as 𝑓 𝑦 𝜃 . This function 𝑓𝑦𝜃 identifies the data generating process that underlies an observed sample of
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