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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. ...
User1865345's user avatar
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0 votes

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 $\inf a_i^2=(\inf a_i)^2$ ...
reyna's user avatar
  • 353
2 votes

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 ...
Evan Stegner's user avatar
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% ...
Richard Hardy's user avatar
3 votes

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 ...
Sextus Empiricus's user avatar
6 votes
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 ...
Sextus Empiricus's user avatar
2 votes

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 ...
Christian Geiser's user avatar
0 votes

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 ...
Sextus Empiricus's user avatar
2 votes

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 ...
AdamO's user avatar
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11 votes

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 ...
cdalitz's user avatar
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0 votes
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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 ...
PBulls's user avatar
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0 votes

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 ...
Mathemagician777's user avatar
3 votes
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 ...
reyna's user avatar
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10 votes

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 ...
Thomas Lumley's user avatar
2 votes

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 ...
Ben's user avatar
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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 ...
Pusto's user avatar
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2 votes

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 ...
seanv507's user avatar
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3 votes

Unbiased Estimator of Largest Mean of Two Normal Distributions

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 ...
Matt F.'s user avatar
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11 votes
Accepted

Bootstrap confidence intervals: proving correctness

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 ...
Thomas Lumley's user avatar

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