# Tagged Questions

61 views

### Maximum likelihood estimation of volume

There is a metric called as the Volume V Can somebody explain to me how to find the value of V, which is the volume of a dynamical system. I need to apply maximum likelihood estimation on V to find ...
58 views

### Unbiased estimator of variance for samples *without* replacement

This is a follow-up question on that one: Could Bessel's correction make sample variance estimation even more biased? I understand that you need Bessel's correction to get an unbiased estimate of ...
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### Could Bessel's correction make sample variance estimation even more biased?

It is well known that Bessel's correction creates an unbiased estimator of variance. What it basically does is divide by $n-1$ instead of $n$. Now what I did is that I chose a few number, like ...
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### Improving an unbiased estimator using the Rao-Blackwell theorem [closed]

Given data following a Bernoulli distribution $Y_1,...Y_n \sim B(1,p)$, we want to measure $\theta = \text{Var}(Y_1)$ I found this unbiased estimator $S^2 = \frac{\sum{(y_i-\bar{y}})^2}{n-1}$ I need ...
320 views

### Unbiased estimator of variance of binomial variable

$Y_{1...n}\sim \operatorname{Bin}(1,p)$, iid, and I need to find an unbiased estimator for $\theta=\operatorname{var}(y_i)$. I did some calculations and I think that the answer is ...
83 views

### Is it possible to have an estimator that is unbiased and bounded?

I have a parameter $\theta$ which lies between $[0,1]$. Let us say that I can run an experiment and obtain $\hat{\theta} = \theta + w$, where $w$ is a standard Gaussian. What I need is an estimate of ...
28 views

### Trying to understand an example where unbiased estimators don't exist

I am new to statistics especially in the topic of estimators and sufficient statistic. I am reading a note which says "unbiasedness is a desirable (but not necessary) property of a good estimator". ...
50 views

### Bias in EM estimation for a mixture of normal distributions

Are the parameter estimates for a mixture of two normal distribution using EM algorithm biased or unbiased? More specifically, if I use the EM-algorithm to obtain ML estimates of $μ_1$, $μ_2$, ...
52 views

### Will two estimators converge to the same answer?

Say I have two estimators for the same quantity and using the same model, $E[f(X)]$. I also know that these two estimators are consistent, meaning, if we have a lot of data, they will be close to the ...
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### Estimating parameters of a normal distribution: median instead of mean?

The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance. However, if there are some outliers, the median and the ...
778 views

### Bias correction in weighted variance

For unweighted variance $$\text{Var}(X):=\frac{1}{n}\sum_i(x_i - \mu)^2$$ there exists the bias corrected sample variance, when the mean was estimated from the same data: ...
459 views

### Parameter estimation of exponential distribution with biased sampling

I want to calculate the parameter $\lambda$ of the exponential distribution $e^{-\lambda x}$ from a sample population taken out of this distribution under biased conditions. As far as I know, for a ...