Tagged Questions

1
vote
0answers
25 views

What coefficient could I use to calculate the relative difficulty of a test in relation to others using only mean and population standard deviation?

I have a series of tests, all of them of different difficulty, and from each of them I get an average score and a population standard deviation; e.g: ...
1
vote
1answer
73 views

Compute the variance of parameter estimates given limited number of samples

I'd like to infer the variance of estimated parameter $\hat\theta$ of the density function of $f(x;\theta)$ given only a limited number of samples $X_1,\cdots,X_n$. Bootstrapping doesn't perform well ...
1
vote
0answers
132 views

Finding the UMVUE of the variance of a gaussian with mean zero

Given $Z_1, ..., Z_n, \sim\mathcal{N}(0, θ^2), θ>0$. Define $X_i=|Z_i|$ and consider estimation of $\theta$ and $θ^2$ on the basis of the random sample $X_1,...X_n$. Find the uniformly minimum ...
7
votes
1answer
263 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: ...
0
votes
0answers
71 views

Maximum of sample variance

Let $X_1, \dots, X_n$ be i.i.d from the interval $[0,1]$. I am interested in situation when the sample variance $$\frac{1}{n-1} \sum_{i=1}^n (X_i - \overline{X})^2$$ (where $\overline{X}$ is sample ...
1
vote
0answers
45 views

How to compute variance of a continuous time sequence?

I am observing two continuous time-series where at every instant in time I may observe a unary event. That is, for each sequence, say $S_1$, I have a data set comprised of $S_1 = (t_0, t_1, ..., t_m)$ ...
2
votes
1answer
96 views

Help computing asymptotic variance of a weird first difference estimator in a fixed effects model

I'm working on an econometrics problem set, and I'm having some major problems computing asymptotic variance for this estimator. I'm considering a fixed-effects model $$ Y_{it} = \beta_1 X_{it} + ...
-1
votes
1answer
406 views

Question regarding sampling, estimation and accuracy [closed]

Let's say there are N chunks of metal, each are 4 inches thick. They are to be hammered and reduced to following best possible sizes: 1, 2, 3 or 4 inches. If we were to use sampling to get an estimate ...
27
votes
1answer
1k 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 ...
8
votes
2answers
350 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 ...
0
votes
1answer
200 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 ...
5
votes
3answers
259 views

A short question on sample variance

Consider estimating the variance of a RV $X$, we start with the sample variance: $$ \begin{array}{ll} V_1 & = \frac{1}{N-1} \sum_{i=1}^N (X_i - \bar{X})^2\\ & = \frac{1}{N-1} ...
3
votes
1answer
930 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 ...
3
votes
2answers
143 views

Understanding variance estimators

I am having trouble understanding the following. Let $\mu$ and $\sigma^2$ be the true mean and variance, $\bar{x}$ and $s^2$ the measured mean and variance for a random variable $x$, where ...
6
votes
1answer
228 views

Estimating the variance of poker win rates

Suppose you have a casino with n poker players. Each player has a win rate - the amount of money he wins or loses per hand. We assume that these win rates are normally distributed with a mean of 0. ...
2
votes
1answer
72 views

Estimating variability of unseen factor

I'm looking at binomial data where I believe that the probability of the outcome is the product of two independent factors. If you think of it as a two step decision, At the first step, there is a ...
8
votes
3answers
2k 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
votes
2answers
180 views

Calculating $Var\left\{(\hat{m}-m)^2\right\}$ for a univariate normal distribution

Suppose $\hat{m} = \frac{1}{N}\sum_{i=1}^{N}(X_i)$ where $X_i \sim N(m,\sigma)$. Are the following steps correct? $Var\left\{(\hat{m}-m)^2\right\} = E\left\{(\hat{m}-m)^4\right\} - ...