# Tagged Questions

63 views

### Asymptotic normality and normalization wrt variance

Let $X_n, n \in \mathbb N$ be a sequence of random variables with finite variances. As $n \to \infty$, are the following two equivalent: $X_n \to N(0, \sigma^2)$ for some $\sigma^2 \in [0, \infty)$, ...
355 views

### Observed information matrix is a consistent estimator of the expected information matrix?

I am trying to prove that the observed information matrix evaluated at the weakly consistent maximum likelihood estimator (MLE), is a weakly consistent estimator of the expected information matrix. ...
165 views

### Asymptotic normality of MLE in exponential with higher-power x

Given the distribution: $f(x;\theta) = \frac{3}{\theta}x^2e^{-x^3/\theta}$ if $x>0$ the MLE for $\theta$ is $\frac{1}{n}\sum_{i=1}^n x_i^3$. It's an unbiased estimator with variance $\theta^2/n$. ...
149 views

### Parameter estimation for the sum of two Independent (not necessarily i.d.) Gamma RVs

I'm a bit of a stats newbie so take it easy on me if this ends up being somehow trivial. I'm working on a problem that involves parameter estimation for the sum of two independent gamma distributions ...
The standard factor model formulation is $y=W x+\epsilon$ where $x \sim \mathcal{N}(0, I)$, $\epsilon \sim\mathcal{N}(0, \Sigma)$. $W$ and $\Sigma$ are typically estimated from MLE. The solution can ...