# Tagged Questions

Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data that has a random component.

45 views

### Bayesian Example

Ex. suppose that $x=2$ denotes the number of successes in $n=5$ independent trials with probability $θ$ of success, that is $x$ has a binomial distribution with the parameters $n=5$ and $θ$. ...
27 views

10 views

65 views

26 views

17 views

### How to use MLE method for non-distribution function?

I understand that maximum likelihood estimation (MLE) method is normally used with distribution function. However is there anyway around I can do to use MLE for a function which is not distribution ...
11 views

### Fisher's information better than covariance matrix in estimators

I know Fishers information matrix is the inverse of covariance matrix. But why is it better to use fishers information matrix instead of covariance matrix in the case of distributed sensor networks?
30 views

28 views

### How could an estimator be biased but consistent according to mathematical definition?

According to the definition, an estimator can be biased, if $E_{\theta}[\hat{\theta}]\ne\theta$, with $\theta$ as parameter for a distribution we want to get from samples. While the estimator can be ...
13 views

### Estimation of binomial probabilities $f(r)$ over $r \in [0,\frac{1}{2}]$

I want to fit a (decreasing) univariate function, $$f(r),$$ over $r \in [0,\frac{1}{2}]$ to a series ($r =\frac{1}{100}, \frac{2}{100}, \frac{3}{100} ,\ldots,\frac{1}{2}$) ...
50 views

### Proving that a statistic is not sufficient (uniform case).

Let $X=(X_1,...,X_n)$ be i.i.d. $U(0,\theta)$. How to show that $$\frac{2}{n}\sum_{i=1}^{n}X_i$$ is not a sufficient statistic? I have already proven that $\max_{i=1,...,n}X_i$ is a sufficient ...
37 views

### IMPROVED - Proving that a statistics is not sufficient (Gaussian case).

Let $X=(X_1,...,X_n)$ be i.i.d. $N(0,\sigma^2)$. How to show that $$\frac{2}{n}\sum_{i=1}^{n}X_i$$ is not a sufficient statistic? I have already proven that $\max_{i=1,...,n}X_i$ is a sufficient ...
26 views

### Show that $\hat{\mu}$ has minimal variance

So two independent analyses of a content in a water sample have been made using two different methods, both without systematical errors but with different standard deviations. Method $B$ is assumed to ...
45 views

### Is “non-random parameter estimation” the same thing as maximum likelihood estimation?

In one book and a few papers, mostly on navigational tracking, I have found reference to the method of "non-random parameter estimation" but this term is not on the Wikipedia and not in a lot of ...
13 views

### How to define a likelihood function for an EM algorithm

Assuming $A$ a set of vectors from a normal distribution, and $X$ a projection matrix and $B$ a set of projected vectors of $A$ using $X$: $B=A*X$ Using an EM approach and by initializing X from ...
20 views

### Checking if estimators are sufficient

For an i.i.d. sample of random variables Xi distributed according to a normal distribution, known variance. I found a sufficient statistic—the sample mean. How do I check if other statistic like (...
Assume we that we calculate the expected value of some measurements $x=\dfrac {x_1 + x_2 + x_3 + x_4} 4$. what if we dont include $x_3$ and $x_4$, but instead we use $x_2$ as $x_3$ and $x_4$. Then We ...