Least squares estimator formula
[DOC File]Least Median of Squares Regression
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Of course, least squares would perform well if we simply threw out the outliers (point Y11 in the Dirty data set example or the points in the lower left-hand corner in the picture above). In fact, this is exactly the strategy adopted by another robust estimator called Least Trimmed Squares, LTS.
[DOC File]Chapter 1 – Linear Regression with 1 Predictor
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Recall that the least squares estimate of the intercept parameter, , is a linear function of the observed responses : Recalling that : Thus, b0 is an unbiased estimator or the parameter 0. Below, we obtain the variance of the estimator of b0.
[DOC File]Derivation of the Ordinary Least Squares Estimator
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In the previous reading assignment the ordinary least squares (OLS) estimator for the simple linear regression case, only one independent variable (only one x), was derived. The procedure relied on combining calculus and algebra to minimize of the sum of squared deviations. The simple linear case although useful in illustrating the OLS ...
[DOC File]Formula Sheet
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The Method of Least Squares. For the linear model : , the Least Squares estimator is comprised of the following 2 formulas (where T is the size of the sample): Note that b2 could also be calculated using one of the other 3 formulas: where . These estimators have the following means and variances: and . and
[DOC File]Derivation of the Ordinary Least Squares Estimator
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As briefly discussed in the previous reading assignment, the most commonly used estimation procedure is the minimization of the sum of squared deviations. This procedure is known as the ordinary least squares (OLS) estimator. In this chapter, this estimator is derived for the simple linear case.
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There are (at least) three possible estimators for the asymptotic covariance matrix for this estimator: (1) the usual estimator that you compute when you compute ordinary least squares estimators, (2) the White estimator, and (3) the appropriate estimator based on equation (13-56) in your text in which the terms with unequal subscripts are zero.
[DOC File]Economics 1123 - Harvard University
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The Sampling Distribution of the OLS Estimator (SW Section 5.5) Under the four Least Squares Assumptions, The exact (finite sample) distribution of has mean (1, var() is inversely proportional to n; so too for . Other than its mean and variance, the exact distribution of is very complicated. is consistent: (1 (law of large numbers)
[DOC File]Economics 1123 - Harvard University
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Under the three Least Squares Assumptions, The exact (finite sample) sampling distribution of has mean (1 (“ is an unbiased estimator of (1”), and var() is inversely proportional to n. Other than its mean and variance, the exact distribution of is complicated and depends on the distribution of (X,u)
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