Tagged Questions
1
vote
1answer
33 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 $\sigma^2 \in [0, \infty)$,
...
0
votes
0answers
91 views
Deriving asymptotic distribution
I'm working on a question and I appreciate if you could guide me on how to approach it. Here is the question:
Consider $Y_1, Y_2, \ldots, Y_n$ as iid with density $f(y;\theta)$ and assume that the ...
7
votes
1answer
248 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. ...
2
votes
0answers
139 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 $\theta^2/n$. ...
2
votes
0answers
140 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 ...
4
votes
0answers
90 views
Factor models with small noises
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 ...
10
votes
3answers
492 views
Can the empirical Hessian of an M-estimator be indefinite?
Jeffrey Wooldridge in his Econometric Analysis of Cross Section and Panel Data (page 357) says that the empirical Hessian "is not guaranteed to be positive definite, or even positive semidefinite, for ...
