An Introduction to Regression Analysis
... make the discussion concrete, I will employ a series of illustrations involving a hypothetical analysis of the factors that determine individual earnings in the labor market. The illustrations will have a legal fl avor in the latter part of the lecture, where they will incorporate the possibility th ...
... make the discussion concrete, I will employ a series of illustrations involving a hypothetical analysis of the factors that determine individual earnings in the labor market. The illustrations will have a legal fl avor in the latter part of the lecture, where they will incorporate the possibility th ...
Asymptotic Theory
... (i) if plim(xn ) = θx , then plim(g(xn )) = g(θx ), for any function g(·) that is continuous at θx . This is sometimes called Slutsky’s theorem. (For example, plim(x2n ) = θx2 . plim(1/xn ) = 1/θx unless θx = 0 at which value the function g(θx ) is not continuous.) (ii) if xn converges in distributi ...
... (i) if plim(xn ) = θx , then plim(g(xn )) = g(θx ), for any function g(·) that is continuous at θx . This is sometimes called Slutsky’s theorem. (For example, plim(x2n ) = θx2 . plim(1/xn ) = 1/θx unless θx = 0 at which value the function g(θx ) is not continuous.) (ii) if xn converges in distributi ...
Statistical inference for nonparametric GARCH models Alexander Meister Jens-Peter Kreiß May 15, 2015
... n−1/2 -consistency, asymptotic normality and asymptotic efficiency for the quasi maximum likelihood estimator of the GARCH parameters. Hall and Yao (2003) study GARCH models under heavy-tailed errors. More recent approaches to parameter estimation in the GARCH setting include Robinson and Zaffaroni ...
... n−1/2 -consistency, asymptotic normality and asymptotic efficiency for the quasi maximum likelihood estimator of the GARCH parameters. Hall and Yao (2003) study GARCH models under heavy-tailed errors. More recent approaches to parameter estimation in the GARCH setting include Robinson and Zaffaroni ...
Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix
... and suppose that the parameter of interest is the population regression coefficient. The pseudo-true parameter value of the normal linear model remains the population coefficient for any regression with mean independent disturbances. In contrast, a linear model with, say, disturbances that are mixtures ...
... and suppose that the parameter of interest is the population regression coefficient. The pseudo-true parameter value of the normal linear model remains the population coefficient for any regression with mean independent disturbances. In contrast, a linear model with, say, disturbances that are mixtures ...
OLS with one variable - newamericanpolitics.org
... Least squares assumption #1, ctd. • A benchmark for thinking about this assumption is to consider an ideal randomized controlled experiment: • X is randomly assigned to people (students randomly assigned to different size classes; patients randomly assigned to medical treatments). Randomization is ...
... Least squares assumption #1, ctd. • A benchmark for thinking about this assumption is to consider an ideal randomized controlled experiment: • X is randomly assigned to people (students randomly assigned to different size classes; patients randomly assigned to medical treatments). Randomization is ...
Adaptive Directional Stratification for controlled
... Methods such as sparse grid are currently under development to overcome the curse of dimensionality. However, these methods require smoothness assumptions to be efficient [10, 11, 12]. Consequently, these optimized numerical integration methods, potentially efficient, are inadequate in our context. ...
... Methods such as sparse grid are currently under development to overcome the curse of dimensionality. However, these methods require smoothness assumptions to be efficient [10, 11, 12]. Consequently, these optimized numerical integration methods, potentially efficient, are inadequate in our context. ...
File: c:\wpwin\ECONMET\CORK1
... Consider a particular assumption the validity of which is in doubt. We formulate a null hypothesis which is known to be correct if the assumption is valid, and an alternative hypothesis which is correct if the assumption is not valid. Next, a test statistic is constructed; this statistic will be so ...
... Consider a particular assumption the validity of which is in doubt. We formulate a null hypothesis which is known to be correct if the assumption is valid, and an alternative hypothesis which is correct if the assumption is not valid. Next, a test statistic is constructed; this statistic will be so ...
Six notes on Basic Econometric topics
... exists) of θb(n) is gradually more strongly concentrated around the point θ as the number of observations increases. 2. Consistency Assume that θb(n) is a statistic (a known function of observable stochastic variables), based on n observations. Let us use it as an estimator for the parameter θ in a ...
... exists) of θb(n) is gradually more strongly concentrated around the point θ as the number of observations increases. 2. Consistency Assume that θb(n) is a statistic (a known function of observable stochastic variables), based on n observations. Let us use it as an estimator for the parameter θ in a ...
Additional Exercises
... Nelson and Startz (1990) conclude that if mzu is large relative to mz" = then b IV is concentrated around 1= , rather than the probability limit of zero from part (c). ...
... Nelson and Startz (1990) conclude that if mzu is large relative to mz" = then b IV is concentrated around 1= , rather than the probability limit of zero from part (c). ...
Introduction to Econometrics - San Francisco State University
... In the previous example of a grade in a course, we can de…ne an event A = f92; 93; :::; 100g. If one of the outcomes in A occurs, we say that event A occurred. Notice that A , which reads "A is a subset of ". As another example, suppose that a student fails a course if his grade is below 60. We can ...
... In the previous example of a grade in a course, we can de…ne an event A = f92; 93; :::; 100g. If one of the outcomes in A occurs, we say that event A occurred. Notice that A , which reads "A is a subset of ". As another example, suppose that a student fails a course if his grade is below 60. We can ...
Statistical Methods in Meteorology - Time Series Analysis
... denote search ranges for the X cal lines) and t2-search (solid). of xÃ1 and xÃ2 in the old part. For both parts the ...
... denote search ranges for the X cal lines) and t2-search (solid). of xÃ1 and xÃ2 in the old part. For both parts the ...
Mathematical Economics - Complementary course of BSc Mathematics - IV semester - 2014 Admn onwards
... The term regression was introduced by Francis Galton. In a famous paper “Family Likeness in Stature”, Galton found that, although there was a tendency for tall parents to have tall children and for short parents to have short children, the average height of children born of parents of a given height ...
... The term regression was introduced by Francis Galton. In a famous paper “Family Likeness in Stature”, Galton found that, although there was a tendency for tall parents to have tall children and for short parents to have short children, the average height of children born of parents of a given height ...
ON SELECTING REGRESSORS TO MAXIMIZE THEIR
... Several definitions will be needed. A function g: ×ßm xv ßq will be termed well-behaved if i. g( ,w) is measurable in w for each 0 , ii. g( ,w) is separable; i.e., contains a countable dense subset o, and the graph of g: ×ßm xv ßq is contained in the closure of the graph of g: o×ßm xv ßq. iii. g( ,w ...
... Several definitions will be needed. A function g: ×ßm xv ßq will be termed well-behaved if i. g( ,w) is measurable in w for each 0 , ii. g( ,w) is separable; i.e., contains a countable dense subset o, and the graph of g: ×ßm xv ßq is contained in the closure of the graph of g: o×ßm xv ßq. iii. g( ,w ...
where = impact - World Bank Group
... • some units (individuals, households, villages) get the program; • some do not. ...
... • some units (individuals, households, villages) get the program; • some do not. ...
Notes 10
... Dispersion about the True Mean • For a comparison of the academic performance of this student with the rest of her graduating class, it is good to look at where they are ranked in the class but better to look at this in relation to the dispersion around the mean • How many standard deviations is a ...
... Dispersion about the True Mean • For a comparison of the academic performance of this student with the rest of her graduating class, it is good to look at where they are ranked in the class but better to look at this in relation to the dispersion around the mean • How many standard deviations is a ...
7. Sample Covariance and Correlation
... 29. Show that the minimum mean square error, using the coefficients in the previous exercise, is MSE(A(X, Y), B(X, Y)) = S 2 ( Y ) ( 1 − R 2 ( X, Y )) 30. Use the result of the previous exercise to show that a. −1 ≤ R(X, Y) ≤ 1 b. R(X, Y) = −1 if and only if the sample points lie on a line with neg ...
... 29. Show that the minimum mean square error, using the coefficients in the previous exercise, is MSE(A(X, Y), B(X, Y)) = S 2 ( Y ) ( 1 − R 2 ( X, Y )) 30. Use the result of the previous exercise to show that a. −1 ≤ R(X, Y) ≤ 1 b. R(X, Y) = −1 if and only if the sample points lie on a line with neg ...
Bayesian Analysis - NYU Stern
... Can we deduce these? For this problem, we do have conditionals: p(β|2 ,data) = N[b,2 ( X'X) 1 ] i (y i x iβ)2 p( |β,data) K a gamma distribution ...
... Can we deduce these? For this problem, we do have conditionals: p(β|2 ,data) = N[b,2 ( X'X) 1 ] i (y i x iβ)2 p( |β,data) K a gamma distribution ...
Econometrics-I-24
... truncated above 0 if y i 0, from below if y i 1. (3) Generate β by drawing a random normal vector with mean vector (X'X)-1 X'y * and variance matrix (X'X )-1 (4) Return to 2 10,000 times, retaining the last 5,000 draws - first 5,000 are the 'burn in.' (5) Estimate the posterior mean of β by aver ...
... truncated above 0 if y i 0, from below if y i 1. (3) Generate β by drawing a random normal vector with mean vector (X'X)-1 X'y * and variance matrix (X'X )-1 (4) Return to 2 10,000 times, retaining the last 5,000 draws - first 5,000 are the 'burn in.' (5) Estimate the posterior mean of β by aver ...
Threshold Regression Without Distribution Assumption when the
... of data support are of the same order of magnitude as in the interior of support. These are very appealing properties when we use sub-sample sets to estimate parameters in distinct regimes for a given threshold. Moreover, the procedure can be simplified as a two-step concentrated kernel-weighted le ...
... of data support are of the same order of magnitude as in the interior of support. These are very appealing properties when we use sub-sample sets to estimate parameters in distinct regimes for a given threshold. Moreover, the procedure can be simplified as a two-step concentrated kernel-weighted le ...
Minimax Optimal Alternating Minimization for Kernel Nonparametric
... Tensor modeling is widely used for capturing the higher order relations between several data sources. For example, it has been applied to spatiotemporal data analysis [19], multitask learning [20, 2, 14] and collaborative filtering [15]. The success of tensor modeling is usually based on the low-ran ...
... Tensor modeling is widely used for capturing the higher order relations between several data sources. For example, it has been applied to spatiotemporal data analysis [19], multitask learning [20, 2, 14] and collaborative filtering [15]. The success of tensor modeling is usually based on the low-ran ...
Chapter 4. Method of Maximum Likelihood
... that, under regularity conditions, the ML estimates are consistent, asymptotically normal, and asymptotically efficient. For simplicity, our treatment will be confined to the case of a 1-dimensional parameter. We begin with the following regularity assumptions: (A0) The distributions Pθ of the obser ...
... that, under regularity conditions, the ML estimates are consistent, asymptotically normal, and asymptotically efficient. For simplicity, our treatment will be confined to the case of a 1-dimensional parameter. We begin with the following regularity assumptions: (A0) The distributions Pθ of the obser ...
Heavy Tails of OLS
... basic scaling property for convolutions of random variables with regularly varying distributions. Subsequently, we obtain the regular variation properties for inner products of those vectors of random variables that appear in the OLS estimator of β . The joint distribution of these inner products is ...
... basic scaling property for convolutions of random variables with regularly varying distributions. Subsequently, we obtain the regular variation properties for inner products of those vectors of random variables that appear in the OLS estimator of β . The joint distribution of these inner products is ...
Analysis of Variance
... • We need to add information about degrees of freedom. • Remember the concept…how many parameters can one change and still calculate the statistic. If we want to know the mean, and the know the values, we can calculate the mean. If we know the mean, and we know all the values but one, we can calcula ...
... • We need to add information about degrees of freedom. • Remember the concept…how many parameters can one change and still calculate the statistic. If we want to know the mean, and the know the values, we can calculate the mean. If we know the mean, and we know all the values but one, we can calcula ...
10.2 Suppose you have T=2 years of data on the same group of N
... Unlike using random effects, we cannot include time-constant variables (even if they can be observed) in estimating the model, since time-constant variables are eliminated from the transformed time-demeaned equation. With fixed effects the time-constant variables, both observed and unobserved, are e ...
... Unlike using random effects, we cannot include time-constant variables (even if they can be observed) in estimating the model, since time-constant variables are eliminated from the transformed time-demeaned equation. With fixed effects the time-constant variables, both observed and unobserved, are e ...
Linear Least Squares Analysis - Society for Industrial and Applied
... Large values of F = MS /MSp support the alternative hypothesis that the simple linear model does not hold. For an observed ratio, fobs , the p value is P(F ≥ fobs ). For example, assume the spruce trees data (page 210) satisfy the general assumptions of this section. Table 14.1 shows the results of ...
... Large values of F = MS /MSp support the alternative hypothesis that the simple linear model does not hold. For an observed ratio, fobs , the p value is P(F ≥ fobs ). For example, assume the spruce trees data (page 210) satisfy the general assumptions of this section. Table 14.1 shows the results of ...