Linked Questions

20
votes
1answer
11k views

What is the standard error of the sample standard deviation?

I read from there that the standard error of the sample variance is $$SE_{s^2} = \sqrt{\frac{2 \sigma^4}{N-1}}$$ What is the standard error of the sample standard deviation? I'd be tempted to guess ...
7
votes
1answer
1k views

Bounds for the population variance?

Suppose we have i.i.d. samples $x_1$, $\ldots$, $x_n$ for a (potentially non-normal) random variable $X$ with finite moments. We can use these samples to construct an unbiased estimates of the ...
6
votes
1answer
359 views

Comparison between MAD and SD

I am reading Huber's Robust Statistics (2nd). On page 2 and 3 he gave an example. The basic facts are summarized here. Let $(X_n)$ be a sequence of random variables and define two measures of spread ...
5
votes
1answer
4k views

Question about standard deviation and central limit theorem

I have a quick question about the central limit theorem. Lets say I measure some value that comes from an arbitrary distribution N times and I repeat this M times. I understand that if I calculcate ...
4
votes
2answers
1k views

Maximum Likelihood Estimation

If $V_1, V_2,\ldots V_{n_1}$ and $W_1, W_2,\ldots,W_{n_2}$ are independent random samples of size $n_1$ and $n_2$ from normal populations with the means $\mu_1$, $\mu_2$ and the common variance $\...
1
vote
1answer
284 views

Proving Asymptotic distribution of $\sqrt n( \widehat\sigma^2 -\sigma^2)$

I am looking at trying to derive an expression for the asymptotic distribution. We have $X_1,\ldots, X_n$ i.i.d $N(\mu, σ^2)$. So we have defined $\hat \sigma^2 = \frac 1n \sum_{i=1}^n(X_i-\mu)^2$. (...
1
vote
0answers
384 views

Asymptotic distribution of sample variance of uncorrelated non-normal sample

I know from this post, that Asymptotic distribution of sample variance of i.i.d non-normal sample that the sample variance $s^2$ is distributed as follows: $$\sqrt n(s^2 - \sigma^2) \rightarrow_d N\...
1
vote
0answers
44 views

Using $\chi^2$ result to find asymptotic distribution of $S^2$ when $X_i$ normally distributed

At the end of this answer it is mentioned that Note: the above result of course holds also for normally distributed samples -but in this last case we have also available a finite-sample chi-square ...
0
votes
1answer
79 views

Expressions for standard error

Most of the statistics textbooks claim that point estimator $\hat\theta_n(\mathbf{X})$ is asymptotically normal if $$\sqrt{n}(\hat\theta_n - \theta) \, \overset{d}{\longrightarrow} \, \mathcal{N}(0, \...
0
votes
0answers
37 views

Distribution of sample standard deviation [duplicate]

I understand that if $X \sim N(\mu, \sigma^{2}$), then the sample mean for a sample size of N is $\overline{x} \sim N(\mu, \frac{\sigma^{2}}{N})$ but I am not sure how was this derived $ \overline{\...