Có 20+ tài liệu thuộc chủ đề "kinh tế ứng dụng"
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PHƯƠNG SAI THAY ĐỔI. Bản chất của phương sai thay đổi Các hậu quả của phương sai thay đổi Phát hiện phương sai thay đổi. Cách khắc phục phương sai thay đổi. Mô hình sai số chuẩn điều chỉnh phương sai thay đổi của White. 9.1 BẢN CHẤT CỦA PHƯƠNG SAI THAY ĐỔI. Sử dụng đồ thị để phân biệt...
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Lecture 1: Normal Distribution. For many random variables, the probability distribution is a specific bell-shaped curve, called the normal curve, or Gaussian curve. 1) Standard normal distribution. The standard normal distribution has the probability density function as follows:. 2 1 2 Features of the curve are:. 1) z 2 increases in the negative exponent. 3) The standard deviation is one...
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1) Assumptions of the two-variable linear regression model. ∑e i 2 = ∑(Y i – b 0 – b 1 X i ) 2 → min The resulting estimators of b 0 and b 1 are then given by:. TSS is the total sum of squares, which is observed in the dependent variable Y RSS is the residual sum of...
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‘Life is the art of drawing sufficient conclusions from insufficient premises’. The estimates of the regression parameters are influenced by a few extreme observations. We may use the residual plot to find the outlier, which are inadequately captured by the regression model itself.. ¾ The percentiles that cut the data up into four quarters have special names: The 25 th...
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Frequently, one may wish to include the quality independent variables, often called dummy variables, in the regression model in order to (i) capture the presence or absence of a. It is normally used as a regressor in the model.. The assumption made in the dummy variable method is that it is only the intercept that changes for each group but...
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Lecture 5: Simple versus Multiple Regression. 1) Multiple regression model. Multiple regression is the extension of simple regression, to take account of more than one independent variable X. 2) Simple versus multiple regression. Example 1: In a fertility survey of 4700 Fiji women (Kendall and O’ Muirchearttaigh, 1977) the following variables were observed for each women.. AGE : women’s present...
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The variance of the least squares estimator of the slope coefficient of a multiple regression is given by:. where R j 2 is the coefficient of determination of the auxiliary regression of X j with all the regressors included in the model. The variance of the estimator of the slope coefficient (V(β j. (1) Since the simpler model features less...
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Multiple regression is impossible in the presence of perfect collinearity or multicollinearity. One of the variables must be dropped. When the multicollinearity is present, the interpretation of the coefficients will be quite difficult.. 2) Practice consequences of multicollinearity. The easiest way tell whether multicollinearity is causing problems is to examine the standard errors of the coefficients. If several coefficients have...
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Autocorrelation (also called serial correlation) is violation of the assumption that the error terms are not correlated, i.e., with autocorrelation E(∈ i. That is, the error in the period t is not independent of previous errors.. The positive autocorrelation is the common problem in economics.. Autocorrelation can show up in the residual plot. We can formalize this approach in the...
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is a false statement for any object x. (The choice of notation is motivated by the fact that the power set of a set that contains m elements has exactly 2 m elements.) For instance, 2. for any set S.. for any sets A and B. (A ∪ C), for any sets A, B and C.. Given any two sets...
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The former one is put to good use in the last section of the chapter which provides an introduction to ordinal utility theory, a topic that we shall revisit a few more times later. The Schröder-Bernstein Theorem is, in turn, proved via the Tarski Fixed Point Theorem, the first of the many fixed point theorems that are discussed in this...
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We begin with the formal definition of a metric space.. When the (semi)metric under consideration is apparent from the context, it is customary to dispense with the notation (X, d), and refer to X as a metric space.. It is easy to check that (X, d) is indeed a metric space. R n , d p ) is a metric...
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0 (which may depend on both ε and x) such that. ε for any y ∈ R. N ε, R (f (0)) for any ε >. 0 for all y ∈ O.. 0 for all x ∈ X \ A.. 0 such that. ϕ n (x)) is continuous. φ i ◦ π i is continuous (for each i). t i...
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Some of these fixed point theorems are put to good use in the final section of the chapter where we elaborate on the notion of Nash equilibrium. [1] For any n ∈ N , p ∈ R n. for any x ∈ X. This correspondence contains all the information that has: y x iff y ∈ U (x) for any...
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Let us first recall that a binary operation • on a nonempty set X is a map from X × X into X, but we write x • y instead of • (x, y) for any x, y ∈ X (Section A.2.1).. For any group (X. (x 1 y 1 − x 2 y 2 , x 1 y 2...
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Let X be a linear space and T a nonempty convex subset of X. Γ(x) for all x ∈ X.. [1] Any linear subspace C of a linear space X is a convex cone. H Let C be a cone in a given linear space. such that x = λy. H Let C be a nontrivial convex cone in a...
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Metric Linear Spaces. This leads us to the notion of metric linear space. 1 Metric Linear Spaces. Take a linear space X. Let X be a linear space. then X is called a metric linear space. A metric linear space X is said to be nontrivial if X. 4 So, it follows from Proposition 1 that X is a metric...
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Normed Linear Spaces. 1 Normed Linear Spaces. Let X be a metric linear space. Let X be a metric linear space with (1. In a metric linear space X with (1), would we necessarily have (2)?. 1.2 Normed Linear Spaces. Let X be a linear space. is a normed linear space. is called a seminormed linear space. and refer to...
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Differential Calculus. 1 Fréchet Differentiation. Suppose f is differentiable at x, that is, there is a real number f (x) with. It follows that f is differentiable at x, and f (x. This elementary argument establishes that f is differentiable at x iff there is a linear functional L on R such that. a map Φ : T → Y...
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Chapter C Metric Spaces C.1 Basic Notions. Compactness C.6 Fixed Point Theory I. 2 The Banach Fixed Point Theorem. 3 ∗ Generalizations of the Banach Fixed Point Theorem C.7 Applications to Functional Equations. 4 ∗ Remarks on the Differentiability of Real Functions 5 A Fundamental Characterization of Continuity 6 Homeomorphisms. 3 Weierstrass’ Theorem D.4 Semicontinuity. 1 ∗ Caristi’s Fixed Point...