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Questions tagged [blue]

Best Linear Unbiased Estimator

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0answers
12 views

Heteroskedasticity testing

Im estimating the carhart 4 factor model. Im testing for heteroskedasticity to see whether i need to use adjusted standard errors, but i am finding conflicted results. All but one test (ARCH) are ...
2
votes
2answers
285 views

Why use OLS when it is assumed there is heteroscedasticity?

So I'm slowly going through the Stock and Watson book and I'm a bit confused on how to deal with the issue of homoscedacity/heteroscedacity. Specifically, it is mentioned that economic theory tells ...
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0answers
20 views

Estimability in Design model

consider the design model $y=\theta+e$ I know we can obtain the normal equations from observation to estimate the parameters. my question is- is the estimation BLUE? Given normal equations are: $...
0
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1answer
49 views

In a mixed model (asreml), are coefficients and predictions the same?

I am using asreml-R to model genotypic effects of crop field trials and I am confused on how to get best linear unbiased estimates for crop varieties of the model. I've found two different ways how ...
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0answers
17 views

Straddles across earnings [closed]

Hi everyone I have a data set composed of about 25 variables in which the goal is to predict how much the stock will move after it reports earnings. I am getting alot of heteroskedasticity in the data....
4
votes
0answers
240 views

Is the OLS estimator the UMVUE (assuming Normality)?

Suppose $$ \mathbf{y} = \mathbf{X} \mathbf{b} + \mathbf{e} \, , \\ \mathbf{e} \sim \mathcal{N}(0,\mathbf{I}_P) \, . $$ We know that $\mathbf{\hat{b}} = (\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T \...
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0answers
322 views

Proving OLS estimator is BLUE in simplified model (deriving the variance)

A model is given as $Y = \mu + u_i$ where $u_i $ $IID(0,\sigma^2)$ with a sample of $n$ observations. I have to prove that the OLS estimator for $\mu = \frac{\sum Y_i}{n}$ is the BLUE estimator. I ...
2
votes
1answer
133 views

What's the difference between “Optimal linear predictor” and “best unbiased linear estimator”?

Greene (econometric analysis 7th ed. p 53) states that OLS is the "optimal linear predictor": Then on the next page, he states that OLS is also the BLUE estimator (Gauss-Markov Theorem): I ...
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0answers
26 views

deduce variance from precision for bathymetry dataset

I mean to merge 2 gridded dataset of bathymetry using BLUE (Best Linear Unbiased Estimate). $merged = \frac{(\sigma_1^2 * dataset2 + \sigma_2^2 * dataset1)}{(sigma_1^2 + sigma_2^2)}$ I know the ...
8
votes
2answers
842 views

What are the properties of MLE that make it more desirable than OLS?

This question seems fundamental enough that I'm convinced it has been answered here somewhere, but I haven't found it. I understand that if the dependent variable in a regression is normally ...
0
votes
1answer
2k views

Is OLS estimator the only BLUE estimator?

Gauss–Markov_theorem states that OLS estimator is a BLUE estimator. My doubt is can there be any other linear estimator, other than OLS, which is also a BLUE estimator? After going through the proof ...
6
votes
1answer
1k views

Why is bias equal to zero for OLS estimator with respect to linear regression?

I understand the concept of bias-variance tradeoff. Bias based on my understanding, represents the error because of using a simple classifer(eg: linear) to capture a complex non-linear decision ...
1
vote
1answer
1k views

Proof that an estimator is linear

can u guys give some hint on how to prove that tilde beta is a linear estimator and that it is unbiased? $$\tilde\beta=\frac1n\sum_{i=1}^n\frac{y_i-\bar{y}}{x_i-\bar{x}}$$ i have attempted to ...
4
votes
1answer
790 views

Role of Gauss-Markov Theorem in Linear Regression

How does being BLUE matter in Linear Regression for the coefficients? What does Heteroscedasticity Consistent & Auto-correlation Consistent Dispersion matrix take care off in this regard?
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0answers
207 views

Derivation of BLUE estimator under Heteroskedasticity

Firstly, I want to thank you, for being here. Secondly, I wanna apologize for my lack of coding abilities, this question would have been so much more presentable if I was capable of it! By ...
2
votes
1answer
759 views

Restricted OLS have less variance than OLS?

According to Gauss-Markov Theorem, ordinary least squares (OLS) is the best linear unbiased estimator (BLUE). How then can restricted OLS have less variance? Please tell me the reason.
12
votes
1answer
2k views

Other unbiased estimators than the BLUE (OLS solution) for linear models

For a linear model the OLS solution provides the best linear unbiased estimator for the parameters. Of course we can trade in a bias for lower variance, e.g. ridge regression. But my question is ...
1
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0answers
139 views

Combining variance reduction techniques

I'm looking for some reference on the combination of various variance reduction techniques, in particular a best linear unbiased estimator. The only reference I have is McLeish - Monte Carlo ...
1
vote
1answer
817 views

How to Estimate the Error Term in a Heteroscedastic Model with Regression Through the Origin

Suppose we have a NO INTERCEPT model, $$y_i=\beta x_i+e_i$$ where $e_{i}$ follows a N(0,$\sigma^2 x_i^h$), so $e_i$ is equal in distribution to $e_{0i} x_i^{\frac{h}{2}}$, where $e_{0i}$ follows a N(...
20
votes
1answer
10k views

Why do the estimated values from a Best Linear Unbiased Predictor (BLUP) differ from a Best Linear Unbiased Estimator (BLUE)?

I understand that the difference between them is related to whether the grouping variable in the model is estimated as a fixed or random effect, but it's not clear to me why they are not the same (if ...
7
votes
3answers
7k views

Proving Linear Estimator (beta) is BLUE?

In the book Statistical Inference pg 570 of pdf, There's a derivation on how a linear estimator can be proven to be BLUE. I got all the way up to 11.3.18 and then the next part stuck me. After ...
4
votes
1answer
2k views

Proof for “Least squares estimator is BLUE”

I checked all the books and on-line materials I could find for the proof, but found all of them have a derivation problem, which I cannot understand. To prove the least squares estimator is the $...
8
votes
2answers
2k views

Gauss-Markov theorem: BLUE and OLS

I'm reading up on the Guass-Markov theorem on wikipedia, and I was hoping somebody could help me figure out the main point of the theorem. We assume a linear model, in matrix form, is given by: $$ y =...
4
votes
2answers
4k views

Why doesn't the Cramer-Rao lower bound apply?

Let $X_1, X_2, \dots, X_n$ be a sample of i.i.d. random variables, with density $$f_\theta=\frac{2}{3\theta}\left(1-\frac{x}{3\theta}\right) $$ for $0 < x < 3\theta$. And $f_\theta=0$ if $ x <...