# likelihood function

1. ### Inference Statistic - Likelihood Function

## LaTeX Code Can anyone help me understand this? Consider the four observations from de Normal Distribution with variance equal to one $y_1 < 10$$, y_2 > 10$, $5 < y_3 < 10$ and $y_4 = 10$. The likelihood function is? Would be: \$ \prod_{1}^{4} \frac{1}{\sqrt(2\pi)}\exp{-\frac{(y_i...
2. ### log likelihood function ARMA

To derive the log-likelihood function of an MA(1) we condition on \epsilon_0 . But when deriving the log-likelihood function function for an AR(1) we don't. Why not? Is it just because \epsilon_0 isn't found in the AR(1) equation?
3. ### PDF of (nearly) collinear variables

My question is motivated by a problem with estimation by maximum likelihood. In simple terms, I want to estimate a parameter \beta and have three variables, X, Y and Z, such that Z = X+Y. Using all three variables is pointless and the joint pdf is singular. Now, suppose that instead of Z I have...