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 $\... 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 ... 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 ... 1answer 383 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 ... 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 ... 1answer 325 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$\hat \sigma^2 = \frac 1n \sum_{i=1}^n(X_i-\mu)^2$. (... 1answer 83 views ### Expressions for standard error Most of the statistics textbooks claim that point estimator$\hat\theta_n(\mathbf{X})$is asymptotically normal if $$\sqrt{n}(\hat\theta_n - \theta) \, \overset{d}{\longrightarrow} \, \mathcal{N}(0, \... 0answers 424 views ### Asymptotic distribution of sample variance of uncorrelated non-normal sample I know from this post, that Asymptotic distribution of sample variance of i.i.d non-normal sample that the sample variance s^2 is distributed as follows:$$\sqrt n(s^2 - \sigma^2) \rightarrow_d N\... 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 ... 0answers 15 views ### Limiting distribution of sample variance and standard deviation I have a centered Gaussian sample of$n$elements$X_i,\,i=1,..,n$, with variance$\sigma^2$. I would like to find the limiting distribution of the sample variance$\sigma_n^2=\frac 1n \sum_{i=1}^n ...
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{\...