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Results tagged with least-squares
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user 76484
Refers to a general estimation technique that selects the parameter value to minimize the squared difference between two quantities, such as the observed value of a variable, and the expected value of that observation conditioned on the parameter value. Gaussian linear models are fit by least squares and least squares is the idea underlying the use of mean-squared-error (MSE) as a way of evaluating an estimator.
2
votes
While deriving Least Squares Estimators, how to find the derivate of a summation operate?
We have
\begin{align*}
\frac{d}{d\hat\alpha}\sum_{i=1}^n(y_i-\hat\alpha-\hat\beta x_i)^2
&=\sum_{i=1}^n\frac{d}{d\hat\alpha}(y_i-\hat\alpha-\hat\beta x_i)^2\\
&=\sum_{i=1}^n2(y_i-\hat\alpha-\hat\beta …
- 6,039
0
votes
Measuring the causal impact of a policy that is not binding
Let $I$ be the variable of whether a company takes the insurance policy or not, and let $Y$ be the effect you wish to measure. Let $U_Y$ be the exogenous variable giving rise to the error term. Then a …
- 6,039
5
votes
1
answer
541
views
Zero Covariance vs Independence of Slope and Intercept Estimators in Linear Models with Leas...
$\newcommand{\Cov}{\operatorname{Cov}}$Problem Statement: Under the assumptions of Exercise 11.16, find
$\Cov\big(\hat\beta_0,\hat\beta_1\big).$ Use this answer to show that
$\hat\beta_0$ and $\hat\be …
- 6,039
4
votes
Does an endogenous variable bias the coefficient of the exogenous one?
Well, except in the multivariate normal case, zero covariance does not imply independence. You have not specified any distributions, so we cannot assume multivariate normal distributions. So technical …
- 6,039