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1 vote

Different Transformation of the same IV

I agree with everything Nick said here (except that I still use "independent variable"). I'd just add that, unless you have strong substantive reasons for your somewhat unusual choice, then ...
Peter Flom's user avatar
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2 votes

Different Transformation of the same IV

Naturally it's possible. You did it. Your question is presumably whether it's a good idea. Question in turn: Why did you choose different transformations in different models? There are many myths ...
Nick Cox's user avatar
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0 votes

Help clarify the implication of normality in an Ordinary Least Square (OLS) Regression

The original claim probably implied or mentioned elsewhere that the conditional distributions have constant variance. However, without that assumption, the claim is false, as the below simulation ...
Dave's user avatar
  • 65k
0 votes

OLS vs MLE when errors are not normally distributed (Laplace distributed)

OLS is BLUE regardless of the distribution of the errors, as long as they have a finite variance. However, the "Best" in BLUE refers to a specific criterion: variance, or, equivalently in ...
jbowman's user avatar
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8 votes

A model suffering from omitted variable bias can be said to be unidentified?

From the tag: A model is identifiable if a single set of parameters can be found that will yield the best fit. Unidentifiability is typically used to mean the model can't uniquely assign values to ...
Frans Rodenburg's user avatar
2 votes

Deriving $k_i$ for $\hat{\beta} = \sum_{i=1}^n k_i y_i$ where $\hat{\beta}$ is the OLS -estimator

Thank you all for the answers! I've come up with a derivation in scalar form after many trials and errors and decide to post my own attempt here. Now that I'm not entirely sure of my solution and I'm ...
Roger Jia's user avatar
4 votes
Accepted

Deriving $k_i$ for $\hat{\beta} = \sum_{i=1}^n k_i y_i$ where $\hat{\beta}$ is the OLS -estimator

Using the vector approach in the linked question and answer, we can derive a general result for multiple linear regression and then derive the special case of interest for simple linear regression. ...
Ben's user avatar
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2 votes

Deriving $k_i$ for $\hat{\beta} = \sum_{i=1}^n k_i y_i$ where $\hat{\beta}$ is the OLS -estimator

I am not going to engage in vectorial arguments for they are already stated in other answers and primarily due to the fact that what OP asked warrants a simpler treatment. C&B offers a ...
User1865345's user avatar
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2 votes

Are least squares equivalent to ML normal distribution for any $f$?

Least Squares Estimation (LS) The least squares estimation aims to minimize the sum of squared residuals between the observed values $ y_i $ and the model predictions $ f(x_i, \beta) $: $$ LS = \arg\...
Robert Long's user avatar
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3 votes
Accepted

Question about OLS estimator (BLUE proof)

Note that we are constructing a general proof that applies to all possible regression problems (subject to the usual conditions, e.g., homoskedasticity of the errors) , not proving unbiasedness for a ...
jbowman's user avatar
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10 votes
Accepted

What does it mean for observations to be uncorrelated and have constant variance?

These are assumptions made for certain models to ensure certain properties, like valid test statistics. There's a great overview here. The key word here is assumption. These need not hold up in real ...
Frans Rodenburg's user avatar
7 votes

What does it mean for observations to be uncorrelated and have constant variance?

$y_i$'s are not just real numbers. They are random variable. Specifically, the simplest linear model assumes $$y_i = x_i^T\beta+\varepsilon_i,\quad \varepsilon_i\overset{iid}{\sim}\mathcal{N}(0,\sigma^...
Voyager's user avatar
  • 305
10 votes

What does it mean for observations to be uncorrelated and have constant variance?

Random variables VS observations. Strictly speaking, there are random variables (which take values in $\mathbb{R}$) and realizations of these random variables (which are elements of $\mathbb{R}$). ...
Idontgetit's user avatar
0 votes

Kalman Filter to minimize weighted errors on the states: what's wrong with my derivation

TL;DR: I think the mistake lies in the incorrect assumption that the weighting matrix $\Omega$ can be factored out and canceled in the optimisation. Rather, it should show how the weights directly ...
Robert Long's user avatar
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