Tagged Questions
1
vote
0answers
30 views
Cramer-Rao bound for $\chi^2$ distribution parameter estimates.
I've stuck in unpleasant problem with noncentral $\chi^2$ distribution.
I work with random variables, distributed as $\chi^2_{\nu}(\lambda)$, where $\nu$ is the degree of freedom and $\lambda$ is ...
6
votes
2answers
178 views
Intuitive explanation of a definition of the Fisher information
I'm studying statistics. When I read the textbook about Fisher Information, I couldn't understand why the Fisher Information is defined like this:
$$I(\theta)=E_\theta\left[-\frac{\partial^2 ...
0
votes
1answer
112 views
how can I get minimum error probability for this decision problem?
I have the decision problem for 4 hypotheses as follows:
$$H_j: Y_k=N_k-s_{jk},\ k=1,2,\ldots,n;\ j=0,1,2,3.$$
where signals are $s_{jk}=E_0\sin(w_cT(k-1)+(j+\frac{1}{2})\frac{\pi}{2}).$ $$$$
In ...
1
vote
1answer
47 views
Proving that the sum of Good-Turing estimators is $1$
I want to know how to go about proving that the Good-Turing estimator has a total probability of $1$. I have seen this proof (page 2) but I found unclear the first step:
$$\sum_j \theta[j] = \sum_r ...
0
votes
2answers
338 views
Exponential Distribution Maximum Likelihood
I found the following question in a past exam paper and I would like to ask how to solve it as I can't find anything in the notes related to it:
...
0
votes
1answer
65 views
Proof of convergence of a sum of mean-consistent estimators
After a few weeks off I am back at my self-study of Measure-Theoretic probability. As always, I thank the community for any detail and answers they can provide as I try to work myself through these ...
2
votes
0answers
76 views
Likelihood Function of Random Process
Given the following data:
$$
x(t) = A + \omega(t)
$$
where $ \omega(t) $ is an AWGN with zero mean, what would be likelihood function $p(x(t);A)$?
I know it could be proven to be:
$$
p(x;A) = C ...
0
votes
0answers
405 views
Maximum likelihood estimation,
Given a problem, we are asked to use a statistical method to come up with a conclusion. e.g. XYZ drug decreases heart diseases. (null hypothesis)
After searching on internet, I got a list of these ...
