The answer given by miura is not entirely accurate so I am answering this old question for posterity: (2). These are very different things. The empirical cdf is an estimate of the CDF (distribution) ...

The validity of the BH procedure depends on the hypothesis tests being positively dependent. If you read their 2001 paper you would see that it is not necessary to be multivariate normal, they gave ...

You must specify a model. You cannot estimate the model or generate a distribution function given the summary statistics. If you had the data, you could at best do non-parametric estimation, e.g. ...

This is a closed testing procedure, so you must correct the p-values to control type-one error within levels of the hypothesis hierarchy. for example, in a normal ANOVA, you test the global null first ...

I think an easier way to think of it is: If there is any variable $C$ $(0<P(C)<1)$ such that the occurrence of $C$ increases the probability of both $A$ and $B$, then $A$ and $B$ cannot be ...

Bootstrapping is naturally a way of estimating the parameters under the alternative, not under the null. As such it does not immediately lend itself to hypothesis testing. In order to perform ...

Actually, I have heard a rumor that decent learning machines are usually better than experts, because the human inclination is to minimize variance at the expense of bias (oversmooth), leading to poor ...

I would discourage you from using density estimation in such a small data set. In non-parametric density estimation, the bias is on the same order as the variance, which generally is OK if and only if ...

I have never heard it suggested to use a mid p-value. This will not necessarily control your type-one error. As previously stated, the correct way to achieve a size of .05 is to perform a randomized ...

I don't understand your data very well, but I can tell you that an alternative to the multinomial bootstrap that works better for rare events is perturbation / wild bootstrap. Perturbation is ...

If you can't derive Cov(mu, tau) you can bootstrap the statistic of interest, i.e. mu+tau (note that the standard bootstrap may not be valid for non-iid data)

I would suggest functional data analysis but I suspect you might have a lot of families with too few children to get reasonable estimates. Go ahead and read into it though, as it addresses your needs. ...

This is an unsupervised learning task. Here is a very simple idea which if incorrect I hope someone else points out. Feed your ten variables into a PCA to extract 2 PCs. Use the two principal ...

$\bar{X}_t = \frac{(t-1)}{t}\bar{X}_{t-1} + \frac{1}{t}X_t$ so I suppose you could say that if $\frac{1}{t}(X_t - \bar{X}_{t-1}) > \epsilon$, then update. You can make similar formulas for more ...