All Questions
5
questions
4
votes
1
answer
300
views
Cramer-Rao lower bound for the variance of unbiased estimators of $\theta = \frac{\mu}{\sigma}$
Let $X_1, \cdots, X_n$ be a sample from the $N(\mu, \sigma^2)$ density, where $\mu, \sigma^2$ are unknown.
I want to find a lower bound $L_n$ which is valid for all sample-sizes $n$ for the variance ...
- 63
1
vote
1
answer
137
views
Fisher Information for $\bar{X}^2 - \frac{\sigma^2}{n}$ with $X_1, \dots, X_n$ normally distributed
I need to find the Fisher Information for $T = \bar{X}^2 - \frac{\sigma^2}{n}$ with $X_1, \dots, X_n$ normally distributed sample with unknow mean $\mu$ and know variance $\sigma^2$. For this I'm ...
- 111
0
votes
0
answers
286
views
Fisher matrix for a discrete distribution
Let $\mathbf{X} = \{X_1, \ldots, X_n\}$ be a sample of i.i.d. variables following a discrete distribution with parameters $\mathbf{p}^T = (p_1, p_2, p_3)$. How can I find the Fisher information matrix ...
- 405
2
votes
1
answer
675
views
Cramér–Rao Lower Bound and UMVUE for $\frac1{\theta}$
Problem: Find the UMVUE of $\frac1\theta$ for a random sample from the population distribution with density $$f(x;\theta)=\theta x^{\theta-1}$$ and show that its variance reaches the Cramér–Rao lower ...
- 123
1
vote
1
answer
340
views
Confidence interval for a function of the MLE
I am studying an old assignment in which I have calculated the MLE for a sample from an exponential distribution. It then gives the formula for the median of an exponential distribution $\ln(2)/\...
- 13