# Questions tagged [minimum-variance]

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319 views

### Better to Minimize Absolute Error or Sum of Squared Error?

I have an Excel model which predicts the number of customers for a given month. The prediction depends on a churn rate. I have the absolute error (actual vs predicted), along with squared error and ...
34 views

### Minimum Variance Unbiased Estimator of Poisson

Let $X1,X2,.....,Xn$ be iid Poisson random variables with unknown parameter $p>0$. Find the minimum variance unbiased estimator of $e^(-2p)$. I could find two estimators, one by the method of the ...
40 views

### How to find an minimum variance unbiased estimator for an integer parameter?

Consider multiple observations $x[n]$ for an integer parameter $A$ under White Gaussian Noise $w[n]$: $x[n]=A+w[n]; \quad$ $n=0,1,...,N−1$ with $w[n] \sim N(0,σ^2)$. Is it possible to have an minimum ...
77 views

### Proof Sample Variance is Minimum Variance Unbiased Estimator for Unknown Mean

I am trying to prove that the unbiased sample variance is a minimum variance estimator. In this problem I have a Normal distribution with unknown mean (and the variance is the parameter to estimate so ...
27 views

279 views

### How to measure how “good” or accurate a probability distribution is? Entropy, variance or what?

How can one measure the accuracy of the probability distribution of, say, a physical magnitude? I know one good candidate is the entropy, which measures the amount of information one has about the ...
557 views

### How does one minimize the standard deviation to find optimal parameters? [closed]

When doing a generalized least squares fit for a line, one computes the residuals as (y - (m*x + b))**2, where (x,y) are the ...
395 views

### How is this minimum variance worked out for this importance sampling estimator?

I was stuck with the function 17.13 in the open source book deep learning on page 590. For short, the question is that, For the importance sampling estimator: \hat s_q = \frac{1}{n}\sum_{i=1, x^{i}...
111 views

### Maximum likelihood estimator and minimum variance challenge

A random sample of size $n_1$ is to be drawn from a normal population with mean $\mu_1$ and variance $\sigma^2_1$. A second random sample of size $n_2$ is to be drawn from a normal population with ...
60 views

### Good parameter estimates vs good computed moment estimates

Suppose I have a distribution from a known parametric family f(x; θ). I have a sample from that distribution. From the sample, I estimate values for the parameters. Suppose I have estimators that I ...
1k views

### Methods of Proving that a UMVUE does not exist?

Are there efficient methods of showing when a UMVUE does not exist? I can think of the trivial case when no unbiased estimators exist at all. But that's not really interesting. I feel like this ...
672 views

### Are MVUEs and MLEs always functions of a minimal sufficient statistic?

Is it the case that both minimum variance unbiased estimators (MVUEs) and maximum likelihood estimators (MLEs) are always functions of a minimal sufficient statistic? If so, how do we know? If not, ...
642 views

### Minimum-variance unbiased linear estimator

Suppose that it is known that the mean of RV $X_i$ is $\mu_i\theta$, (i = 1, 2,..., n), where $\mu_i$ are known constants, whereas $\theta$ is unknown. Let $\Sigma$ be the variance matrix of the ...