Linked Questions

120
votes
3answers
129k views

What is the difference between a consistent estimator and an unbiased estimator?

I'm really surprised that nobody appears to have asked this already... When discussing estimators, two terms frequently used are "consistent" and "unbiased". My question is simple: what's the ...
55
votes
3answers
48k views

Why is sample standard deviation a biased estimator of $\sigma$?

According to the Wikipedia article on unbiased estimation of standard deviation the sample SD $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$ is a biased estimator of the SD of the ...
55
votes
2answers
46k views

What is the difference between ZCA whitening and PCA whitening?

I am confused about ZCA whitening and normal whitening (which is obtained by dividing principal components by the square roots of PCA eigenvalues). As far as I know, $$\mathbf x_\mathrm{ZCAwhite} = \...
25
votes
2answers
3k views

Is it true that Bayesian methods don't overfit?

Is it true that Bayesian methods don't overfit? (I saw some papers and tutorials making this claim) For example, if we apply a Gaussian Process to MNIST (handwritten digit classification), but only ...
10
votes
3answers
4k views

How can I find the standard deviation of the sample standard deviation from a normal distribution?

Forgive me if I've missed something rather obvious. I'm a physicist with what is essentially a (histogram) distribution centered about a mean value that approximates to a Normal distribution. The ...
14
votes
3answers
1k views

Why does this excerpt say that unbiased estimation of standard deviation usually isn't relevant?

I was reading on the computation of the unbiased estimation of standard deviation and the source I read stated (...) except in some important situations, the task has little relevance to ...
3
votes
2answers
294 views

Square-root transform dependent variable to gaussian for ML problem

I have a ML problem with dependent y-variables that are skew-symmetric to the right. I perform the transformation $\sqrt y$ on my dependent variable before running the ML algorithm, and then make a ...
7
votes
1answer
68 views

Is there any difference between estimating $\sigma^2$ and $\sigma$ in a simulation study?

In a simulation study, is there any difference between $\bullet$ estimating the variance $\sigma^2$, $1000$ times and taking its average, and $\bullet$ estimating the standard deviation $\sigma$, $...
3
votes
2answers
133 views

Should I use a paired sample t-test to compare two methods of measuring absorption lines?

Background I'm doing a research project in astronomy and measuring equivalent widths of absorption lines using Gaussian fits from a star's spectrum in order to determine the star's chemical ...
0
votes
0answers
82 views

Ratio of mean absolute deviation to standard deviation under normal distribution

Can someone show why the ratio is $\sqrt{\frac{2}{\pi}}$ ?
0
votes
2answers
63 views

Monte Carlo simulation or big samples

Suppose that we have a population that behaves as $N(1,\sigma^2)$, and we want to estimate $\sigma^2$. I would like to understand the difference between these two approaches: We take a sample $x_1,\...
1
vote
1answer
61 views

Precision of bone density measurement

I just did a precision study scanning 30 patients twice. The calculator presented the least significant change score, but how do I calculate my precision? For instance, the ISCD states that the ...
0
votes
0answers
66 views

Sample number for confidence intervals of derived quantities

I have two related questions: Assuming (as the extreme case) I measured a quantity (A) just twice, but I know that the values would "become" normally distributed if I measured the quantity repeatedly....
2
votes
0answers
42 views

How many samples are needed to approximate the standard deviation?

Assume you have a random variable $X$ for which you want to compute a $1/4$-approximate $\sigma'$ of $\sigma = \sqrt{\operatorname{Var}(X)}$ (i.e. $|\sigma - \sigma'| \leq \sigma/4$). You can only get ...