TAILIEUCHUNG - Bài giảng Chapter 2: Finite sample properties of the ols estimator

Mời các bạn cùng tìm hiểu unbiased; linearity; efficiency; gauss - markov theorem;. được trình bày cụ thể trong "Bài giảng Chapter 2: Finite sample properties of the ols estimator". Hy vọng tài liệu là nguồn thông tin hữu ích cho quá trình học tập và nghiên cứu của các bạn. | Advanced Econometrics Chapter 2 Finite Sample Properties Of The OLS Estimator Chapter 2 FINITE SAMPLE PROPERTIES OF THE OLS ESTIMATOR I. Y with N 0 CT21 rank X k non-stochastic. s random Y random. 3 XX -1XY 3 is a statistics on a sample 3 is random because Yis random. Being random - 3 has a probability distribution called the sampling distribution. - Repeatedly draw all possible random sample of size n calculate 3 each time. Let explore some statistical properties of the OLS estimator 3 build up its sampling distribution. UNBIASED X X -1X Y X X -1X X s XX -1XX XX -1X sV--------J I 3 XX -1X E 3 E XX -1X Nam T. Hoang University of New England - Australia 1 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 2 Finite Sample Properties Of The OLS Estimator p E X X -1 Xs p X X -1 X E s p 0 E GỒ p p is an estimator of p it is a function of the random sample the element of Y . Note we talk about the sample that means we talk about Y only. Because X is a constant - fix matrix. Repeatedly draw all possible random samples of size n draw Y . The least squares estimator is unbiased for p E s 0 Xis non-stochastic . VarCov P E P - E P P - E p - p XX -1 Xs p p VarCov P E p - p p - p E XX -1 X s X X -1 X s E XX -1 X ss X XX -1 X X -1 X E ss X XX -1 X X -1 X ơ 2 X XX -1 ơ2 X X -1 XX X X -1 s----V---- I 2 XX -1 So VarCov P ơ22 X X -1 For the model Y P2 Xi 2 P3 Xi3 ei p p. P3 2 X X -1 2 IX2 E Xl2 Xl3 12 13 Ed X 2 X 3 IX2 2 ________________1_______________ IX22X2 - IXl2Xl3 2 2 3 2 3 Nam T. Hoang University of New England - Australia 2 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 2 Finite Sample Properties Of The OLS Estimator z Ỉ k 3 7 VarCov r s X s i 3 Var 3 Var 3 s X - X -- s X X i 2 i 3 i i 3 r2 s X2 s i 2 E . _ X X n2 1 - 2 i 3 s Xi2 s X nn r sample correlation between Xi 2 Xi 3 r E 2 1 _ 2 Xi 2 1 - r2 3 determined by i rS T Var 3 T ii. r223 T Var À T iii Variation in Xi2 s XỈ2 T Var P ị iv n sample size T Var 3 ị VarCov 3 ơ2 XX -1

• Kinh tế học
• Bài giảng Finite sample properties of the ols estimator
• Finite sample properties of the ols estimator
• Tìm hiểu unbiased
• Tham khảo linearity
• Statistical inference
• Tìm hiểu suy luận thống kê