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3 questions
7
votes
1
answer
411
views
Estimation of a uniform distribution corrupted by Gaussian noise
Problem definition
I have a dataset composed by $m$ observations $y^{(1)},\dots,y^{(m)} \in \mathbb{R}^2$ generated as follow
\begin{equation*}\begin{aligned}
y &= z + v \newline
z & \sim\...
- 473
0
votes
0
answers
25
views
Separating components of a likelihood maximization
Apologies for the naive question, but I have a problem I would like to solve.
Suppose I have a two dimensional likelihood of the form
$L \propto \exp\{-\frac{1}{2}\} \begin{bmatrix}x & y\end{...
- 1
5
votes
1
answer
303
views
MLE for the maximum of n values that are observed only with noise
Suppose $x_1, ..., x_n$ is a fixed set of real numbers. Let $\epsilon_1, ..., \epsilon_n \sim N(0, \sigma^2)$ be i.i.d. with known $\sigma^2$, and suppose we get to observe only $z_i = x_i + \...
- 2,160