All Questions
Tagged with variance estimation
18 questions
21
votes
4
answers
21k
views
Calculating required sample size, precision of variance estimate?
Background
I have a variable with an unknown distribution.
I have 500 samples, but I would like demonstrate the precision with which I can calculate variance, e.g. to argue that a sample size of 500 ...
- 3,901
13
votes
2
answers
8k
views
Reference for $\mathrm{Var}[s^2]=\sigma^4 \left(\frac{2}{n-1} + \frac{\kappa}{n}\right)$?
In his answer to my previous question, @Erik P. gives the expression
$$
\mathrm{Var}[s^2]=\sigma^4 \left(\frac{2}{n-1} + \frac{\kappa}{n}\right) \>,
$$
where $\kappa$ is the excess kurtosis of the ...
- 3,901
10
votes
1
answer
13k
views
Variance of the reciprocal II
Background
I've recently read the paper
Leo A. Goodman, On the Exact Variance of Products
Journal of the American Statistical Association
Vol. 55, No. 292 (Dec., 1960), pp. 708-713
from where I ...
- 537
4
votes
1
answer
4k
views
What is the distribution of the variance of a sample from an unknown distribution?
I am sampling from a parameter with unknown distribution. I would like to calculate a 95% CI for the standard deviation of the sample.
@cardinal provides a nice general solution for calculating a CI ...
- 3,901
4
votes
1
answer
2k
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 ...
- 6,246
47
votes
1
answer
9k
views
Computing Cohen's Kappa variance (and standard errors)
The Kappa ($\kappa$) statistic was introduced in 1960 by Cohen [1] to measure agreement between two raters. Its variance, however, had been a source of contradictions for quite a some time.
My ...
- 1,003
8
votes
1
answer
956
views
The "correct" way to approximate $\text{var}(f(X))$ via Taylor expansion
tl;dr: There are two commonly reported formulas for approximating $\text{var}(f(X))$, but one is notably better than the other. Since it isn't the "standard" Taylor expansion, where does it come from, ...
- 722
7
votes
1
answer
358
views
What's the maximum expectation of a conditional variance, $E[\operatorname{Var}(X+Z_1 \mid X+Z_2)]$?
Let $X,Z_1,Z_2$ be 3 mutually independent RV's, with $Z_1, Z_2$ assuming $N(0,1)$ distribution. $X$ is constrained to have unit 2nd moment, i.e. $E[X^2] =1$, but may take arbitrary distribution. The ...
- 856
6
votes
1
answer
542
views
Estimate of variance with the lowest mean square error
Regarding estimators of variance from a iid sample of size $n$, Karl Ove Hufthammer says Estimates of variance from an iid sample:
if they do have a normal distribution, dividing by n+1 (sic!) ...
- 19.8k
5
votes
2
answers
786
views
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 $1,2,3,...
- 6,246
5
votes
1
answer
353
views
An unbiased estimator of σ³
As it was suggested in the linked answer, $s_n = \sqrt{\frac{\sum_{i = 1}^n (x_i - \bar{x})^2}{n - 1}}$ is not an unbiased estimator of $\sigma$.
I suspect neither $s_n^3 = \sqrt{\frac{\sum_{i = 1}^n ...
- 363
4
votes
1
answer
174
views
How can population variance be estimated from a bivariate sample?
Let's assume a bivariate population with a correlation $\rho$ and a common $\sigma$ so that $\Sigma = \sigma^2 \begin{pmatrix}1 & \rho \\ \rho & 1\end{pmatrix}$.
I would like to know the ...
- 351
3
votes
1
answer
101
views
Ideal Settings for Longitudinal Models?
The way I see it, logically speaking - Longitudinal Data (e.g. medical patients being measured repeatedly over a period of time) can have one of two forms:
Case 1: All patients are measured exactly &...
3
votes
1
answer
185
views
Estimating counts from sampled data
I am working on counting events from sampled web logs. To formalize the problem, consider a random process in which we randomly record an event with known probability $r$. Say we have $n$ recorded ...
- 31
3
votes
1
answer
8k
views
Variance of the $\hat{\sigma}^2$ of a Maximum Likelihood estimator
Given some normally distributed observations $x_1,x_2,...,x_n$
$\forall i\ x_i\sim\mathcal{N}(\mu, \sigma^2)$
the ML estimator decides that the variance that maximizes the likelihood function is (see ...
- 271
3
votes
1
answer
3k
views
How to use method of moment to find Pareto distribution estimator?
I have $f_{\alpha, \beta}(y)=\frac{\alpha}{\beta}(\frac{\beta}{y})^{\alpha +1}, y\ge\beta,\ \ \alpha,\beta\gt 0$. Both $\alpha, \beta$ unknown.
To find estimators using the method of moment, we ...
- 213
3
votes
0
answers
237
views
Estimator of $\frac{\sigma^2}{\mu (1 - \mu)}$ when sampling without replacement
Question
Consider a population of known size $N$, from which we sample $n$ individuals without replacement and measure their trait values $x_i$ for all individual $i$. The variable $x$ is bounded <...
- 5,182
2
votes
1
answer
138
views
What is the name of the distribution of unbiased sample variance for a sample from Gaussian distribution?
Suppose $X_i$'s are iid Gaussian random variables with mean $\mu$ and variance $\sigma^2$.
The distribution of $\sum_i (X_i - \bar{X}_i)^2 / (n-1)$ isn't Chi square. What is its distribution called? ...
- 23