Simultaneous equation methods (econometrics) | Least squares | Regression analysis | M-estimators
In least squares estimation problems, sometimes one or more regressors specified in the model are not observable. One way to circumvent this issue is to estimate or generate regressors from observable data. This generated regressor method is also applicable to unobserved instrumental variables. Under some regularity conditions, consistency and asymptotic normality of least squares estimator is preserved, but asymptotic variance has a different form in general. Suppose the model of interest is the following: where g is a conditional mean function and its form is known up to finite-dimensional parameter β. Here is not observable, but we know that for some function h known up to parameter , and a random sample is available. Suppose we have a consistent estimator of that uses the observation 's. Then, β can be estimated by (Non-Linear) Least Squares using . Some examples of the above setup include Anderson et al. (1976 and Barro (1977). This problem falls into the framework of two-step M-estimator and thus consistency and asymptotic normality of the estimator can be verified using the general theory of two-step M-estimator. As in general two-step M-estimator problem, asymptotic variance of a generated regressor estimator is usually different from that of the estimator with all regressors observed. Yet, in some special cases, the asymptotic variances of the two estimators are identical. To give one such example, consider the setting in which the regression function is linear in parameter and unobserved regressor is a scalar. Denoting the coefficient of unobserved regressor by if and then the asymptotic variance is independent of whether observing the regressor. With minor modifications in the model, the above formulation is also applicable to Instrumental Variable estimation. Suppose the model of interest is linear in parameter. Error term is correlated with some of the regressors, and the model specifies some instrumental variables, which are not observable but have the representation . If a consistent estimator of of is available using as instruments, the parameter of interest can be estimated by IV. Similar to the above case, consistency and asymptotic normality follows under mild conditions, and the asymptotic variance has a different form than observed IV case. Yet, there are cases in which the two estimators have the same asymptotic variance. One such case occurs if In this special case, inference on the estimated parameter can be conducted with the usual IV standard error estimator. (Wikipedia).
Determining the resultant vectors with a scalar
Learn how to determine the resultant vector by adding, subtracting and multiplying vectors by a scalar. We will also learn how to graph the resultant vectors to show the operations. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we add each of the
From playlist Vectors
Graph the resultant vector of the difference of two vectors with a scalar
Learn how to determine the resultant vector by adding, subtracting and multiplying vectors by a scalar. We will also learn how to graph the resultant vectors to show the operations. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we add each of the
From playlist Vectors
Compare Linear and Exponential Growth Using Recursive and Explicit Equations
This video explains the different between linear and exponential growth. Both recursive and explicit equations are discussed. Site: http://mathispower4u.com
From playlist Linear, Exponential, and Logistic Growth: Recursive/Explicit
How to graph and multiply a vector by it's resultant
Learn how to determine the resultant vector by adding, subtracting and multiplying vectors by a scalar. We will also learn how to graph the resultant vectors to show the operations. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we add each of the
From playlist Vectors
What is the formula for the dot product
http://www.freemathvideos.com In this video series I will show you how to apply the dot product of two vectors and use the product to determine if two vectors are orthogonal or not. The dot product does not produce another vector like scalar multiplication but rather produces a scalar tha
From playlist Vectors
How to Quickly Create a Matrix in GeoGebra; How to Multiply 2 Matrices
Creating a matrix in GeoGebra is EASY. You need to use the LIST icons { }. In GeoGebra, a matrix is actually a sequence of lists within a single list. This video shows how.
From playlist Algebra 1: Dynamic Interactives!
Given the scalar difference of two vectors find the resultant vector
Learn how to determine the resultant vector by adding, subtracting and multiplying vectors by a scalar. We will also learn how to graph the resultant vectors to show the operations. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we add each of the
From playlist Vectors
How to find the resultant vector by vector addition
Learn how to determine the resultant vector by adding, subtracting and multiplying vectors by a scalar. We will also learn how to graph the resultant vectors to show the operations. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we add each of the
From playlist Vectors
Model Adequacy Checking (Part C)
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
Recursive Graphs - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Multiple Linear Regression (Part B)
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
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From playlist Coursera Regression V2
02 05 Part 1 of 3 Model Selection
From playlist Coursera Regression V2
sktime - A Unified Toolbox for ML with Time Series
This tutorial is about sktime - a unified framework for machine learning with time series. sktime features various time series algorithms and modular tools for pipelining, ensembling and tuning. You will learn how to use, combine and evaluate different algorithms on real-world data sets an
From playlist Python
Transformation and Weighting to correct model inadequacies (Part A)
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
How To Use The Parallelogram Method To Find The Resultant Vector
This video explains how to use the parallelogram method to find the resultant sum of two vectors. You need to be familiar with law of cosines formula in order to make this work.
From playlist New Physics Video Playlist