# Questions tagged [blue]

Best Linear Unbiased Estimator

25 questions
18 views

### When to use variance stabilizing method?

Let's suppose we want to estimate $p$ from $m$ independant realisations of $X\sim Bin(n,p)$: $x_1,x_2,\dots,x_m$, with respective size $n_i$ $i$ in $\{1,\dots,m\}$. Let $p_i$ be $p_i:=x_i/n_i$. To ...
24 views

### What is relation betwen linearity assumption in OLS and L in BLUE (i.e. OLS is BLUE)

The linearity assumption says that the dependent variable is linear in parameters. When Gauss-Markov assumptions hold, OLS is BLUE, meaning smallest variance amongst Linear Unbiased estimators, where ...
22 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 ...
304 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 ...
22 views

381 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 ...
142 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 ...
30 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 ...
1k 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 ...
3k 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 ...
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 ...
2k 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 ...
872 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?
865 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.
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 ...
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 ...
848 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(...
11k 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 ...