All Questions
Tagged with estimators least-squares
51
questions
4
votes
1
answer
96
views
Mathematical Step for consistency
Let me state my problem from the beginning:
Let $i$ be an index representing countries ($i = {1,2,\ldots,N }$), and $t$ represent time, denoted as available data for country $i$ ($t = {1,2,\ldots,T_i }...
- 309
0
votes
0
answers
10
views
Variations of Correlation Coefficient of Simple Linear Regression with Estimators [duplicate]
Suppose we are using an Ordinary Least Squares (OLS) estimator of $\alpha_{0}$ and $\alpha_{1}$ for the simple linear regression below:
$$
H_{i} = \alpha_{0} + \alpha_{1}X_{i} + \epsilon_{i}
$$
How ...
3
votes
1
answer
144
views
Estimating ratio of regression coefficients
What is the best method of estimating a ratio of regression coefficients $\beta_1/\beta_2$ under the usual assumptions / in practice? I have two relatively well approximated signals $X_1, X_2$ and ...
1
vote
0
answers
137
views
Least squares more efficient than maximum likelihood?
I have synthetic data which is sampled from a non-central chi distribution (similar to what is obtained experimentally). I am fitting a non-linear model to this data to extract three parameters of ...
- 135
6
votes
1
answer
207
views
In OLS, does the uncorrelatedness between regressors and residuals require a constant?
I'm reading this PDF.
It shows how to obtain the OLS estimator and its properties.
It is said that from the normal equations we obtain $X' e = 0$.
Where $X$ is the design matrix and $e$ is the vector ...
- 2,301
0
votes
1
answer
154
views
How did we derive the least square estimator using OLS?
How does multiplying a matrix with its transpose equal "minimizing" it?
When calculating the partial derivative, where does the X' come from?
Why setting the value of third equation to 0 is ...
- 1
3
votes
1
answer
88
views
Consistency of a simple estimator for $y_i = \beta_1 x_i + u_i$
Let $y_i = \beta_1 x_i + u_i$ for $i=1,2,..,n$. If I define $$\hat \beta_1 = \frac{y_1 + y_n}{x_1 + x_n}$$ then whether my $\hat \beta_1$ will be consistent or not in this setup?
For my estimator to ...
- 43
1
vote
0
answers
34
views
Does a linear regression assume that the (unconditional) predictor data is i.i.d?
Say I have a linear, cross sectional relationship -
$y_{i}=x_{i}b+e_{i}$.
Where $E(e_{i}|X_{j})=0$ for all relevant $i,j$. Given this, one can prove that the OLS estimator is unbiased.
However, ...
- 111
1
vote
2
answers
142
views
OLS estimator question: using a subset versus using a dummy-interacted variables
Suppose that we are interested in the following model:
$$y_i=\beta_1+\beta_2x_{i2}+\beta_3x_{i3}+u_i$$
Here, there is a dummy variable $d_i$.
I am wondering whether the following estimators are ...
- 935
1
vote
1
answer
319
views
Do robust estimators like M-estimator still have higher variance than OLS in presence of non-normal errors and/or outliers?
In my studies I've learned that even with non-normality of the errors, the OLS estimator is still considered BLUE (Best Linear Unbiased Estimator). The texts also suggested using M and L estimators ...
- 321
0
votes
0
answers
308
views
Can you explain LINEAR in BLUE?
I have hard time understanding the LINEAR part. Found something like this:
Linear property of OLS estimator means that OLS belongs to that class of estimators, which are linear in Y, the dependent ...
- 131
1
vote
0
answers
43
views
How can I derive OLS predicted error term ^ei as a function of ei?
First of all, I'd like to say that any kind of help would be really helpful, whether it's a hint or a good grad/undergrad book. Right now I'm working with Econometric Analysis of Cross Section and ...
- 11
0
votes
1
answer
64
views
Instrumental variables - OLS - estimation
I have a question regarding the OLS estimation, in the case of an estimation with instrumental variables:
We assume the linear model $𝒚= 𝑿\beta+𝒖$ with $Z$ = instrumental variables.
Multiplying the ...
- 95
4
votes
0
answers
76
views
Proof of invariant angle between $Y$ and $\hat Y$ in $L^2$ regularisation
On this site is the following question which claims that the $L^2$ regularised OLS preserves the angle between $\hat Y$ and $Y$ irrespective of the value $\lambda$. I have not found any source that ...
- 345
1
vote
0
answers
166
views
Asymptotic efficiency of estimators of autoregressive models
Are OLS or MLE estimators of autoregressive model asymptotically efficient if errors are i.i.d?
Consider the case of an AR(1) model $$x_t=\alpha x_{t-1} + \epsilon_t$$
with $\epsilon_t$ ~ $i.i.d. N(0,\...
- 51