# Tag Info

1 vote
Accepted

### Proof of property of Mallows/Wasserstein metric

[I was in the middle of this post when you posted your answer. For future referential purpose, I am completing the draft.] Subadditivity of Mallows distance has been well-documented in many papers. ...
• 7,922

### Proof of property of Mallows/Wasserstein metric

Figured it on my own. Here are some key steps. $[d_2(\sum X_j,\sum Y_j)]^2=(\inf_\pi [E_\pi \{\sum(X_j-Y_j)\}^2]^{1/2})^2=\inf_\pi ([E_\pi \{\sum(X_j-Y_j)\}^2]^{1/2})^2$ as $\inf a_i^2=(\inf a_i)^2$ ...
• 353

### Picking block length in a block bootstrap

Old thread, worthy question. I've treated block length as a hyperparameter to tune, and plotted how it affected the parameter estimate. $n=1$ is a standard i.i.d. bootstrap, so it helped me visualize ...
1 vote

### Does Bootstrapping the Test Set Provide a Real Error Confidence Interval?

Based on the linked thread, I wonder if you might be interested in a prediction interval rather than a confidence interval. A prediction interval is one that contains the prediction error in, say, 90% ...
• 66.3k

### Does Bootstrapping the Test Set Provide a Real Error Confidence Interval?

Would bootstrapping the test set and evaluating many times You do not need to bootstrap the test set. Your test set already contains multiple observations and you evaluate an error for each of them ...
Accepted

### Comparison of confidence intervals: bootstrap & exact resampling

The link in your question describes an exact bootstrap distribution where every possible way of resampling is being computed. For large samples this can be unfeasible due to the amount of computations ...

### Growth Curve Model with time-invariant covariates- standardized CIs

In any multiple regression model--including a growth curve model with multiple correlated covariates of the growth factors--standardized regression (path) coefficients are not bound by [-1, 1]. Unlike ...
• 3,136

### p-values from CIs?

The estimated distribution from a bootstrap method does not always give sufficient information to compute a p-value, and neither a confidence interval. One problem is that p-values (and confidence ...

### p-values from CIs?

A CI can be constructed without a hypothesis. But a $p$-value requires you to state one. Consider, for one, that a difference in standard deviations is not a natural (interpretable) quantity but a ...
• 61.9k

### p-values from CIs?

To compute a p-value with a Monte Carlo test, you must sample values under the null hypothesis and compute the fraction of simulation results that fall beyond the value for the statistic computed from ...
• 4,972
Accepted

### What is the best way to calculate confidence interval for spearman correlation by bootstrapping?

There are a number of issues with your approach, not just with the confidence interval itself: A bootstrap is usually performed by resampling an observed sample. You draw new samples from a ...
• 3,648

### What is the best way to calculate confidence interval for spearman correlation by bootstrapping?

I'm not sure if you took it into account based on only the code you provided, but note that when bootstrapping for a CI for correlation, you have to bootstrap the dependence between the 2 variables as ...
Accepted

### Probability mass function of sample median (Bootstrap)

Hint. $$P_*\left(X_{(m)}^*=X_{(k)}\right)=P_*\left(X_{(m)}^*\ge X_{(k)}\right)-P_*\left(X_{(m)}^*>X_{(k)}\right).$$ To calculate $P_*\left(X_{(m)}^*\ge X_{(k)}\right),$ we observe that this only ...
• 353

### If bootstrap works for $\hat{\alpha}$ and for $\hat{\beta}$, does it work for $\widehat{\alpha\beta}$?

This is more complicated than it sounds, so is a good question. To start off, the bootstrap doesn't work for $\hat\alpha^2$ when $\alpha=0$, which is a classic example of bootstrap failure. The ...

### Appropriate regression model when variables were measured on different subjects?

Consider using an RCT experimental structure with a multilevel model for inference This is quite a fascinating statistical problem. It bears a significant resemblance to standard causal analysis ...
• 123k
1 vote

### Appropriate regression model when variables were measured on different subjects?

It may be useful to try and specify your question in terms of the levels of analysis here. As you've noted, there is no way to map seedling-level bacterial composition to seedling-level root length ...
• 91

### Explanation for the success of bagging

It's also random between draws, to ensure lower $\rho$. In random forests, random subsets of variables (eg $\sqrt{n_{features}}$) are used as candidates to build trees to reduce $\rho$ (ie tree 1 is ...
• 6,624
There is no unbiased estimator, for reasons essentially as in this answer or this answer. Suppose we had the identity $$\max(\mu_x,\mu_y)=E[f(X,Y)]$$ and, in particular, had the right-hand side always ...
How you prove this depends on your statistic $\theta$; there are complicated and straightforward versions depending on how difficult $\theta$ is. Fundamentally, though, the bootstrap works by the ...