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Questions tagged [bootstrap]

The bootstrap is a resampling method to estimate the sampling distribution of a statistic.

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Bootstrap based bias correction

Assume we have a probablistic model $f_{\theta}(x)$ and try to estimate the parameter $\theta$ based on data $x$ with some procedure that yields a biased estimator $$E[\hat{\theta}]=\theta + \eta,$$ ...
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2-sample bootstrap hypothesis test - comparing locations but different estimators in two samples

I have two independent samples X and Y where $x_i \sim F$ and $y_i \sim G$. Two different estimators A and B map X to $x_0$ and Y to $y_0$ respectively. I'd like to compare $x_0$ and $y_0$. The ...
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Multinomial Random Variable - significance test & bootstrapping

If I have a random variable X that follows a multinomial distribution (p1, p2, ..., pn), is there anyway to test if two of the levels have equal probability, for example, if p1 = p2? Also, if I have ...
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bootstrap standard errors - the mean is equal to the observed statistic?

My question revolves around the accuracy of a estimator which is obtained with bootstrap. This example is taken from "An introduction to bootstrap" Efron & Gong: A small experiment, in which 7 ...
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How do I determine the critical r value for Pearson correlation if I compute the result via bootstrapping?

The critical r value for a Pearson correlation analysis depends on sample size. For example, consider a test with the following parameters: n = 20 alpha = .05 I ...
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how to use boot package to do stratified bootstrapping?

Here's a toy data set that replicates my problem. I am interested in knowing the confidence intervals of an empirical distribution that is composed of the scores of each school at the proportion that ...
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Estimating Effective Sample Size in Unequal clustered design (ratio-type estimator)

I'm having trouble understanding how these experimenters calculated their effective sample size. The free article is located in this link here: https://academic.oup.com/icesjms/article/60/2/297/...
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Variance of average of $n$ correlated random variables

Reading about deep leaning, I came across the following formula. $$ \mbox{var} \left( \frac{1}{n} \sum_{i=1}^{n} X_i \right) = \rho \sigma^2 + \frac{1-\rho}{n} \sigma^2 $$ where $X_1, \dots, X_n$ ...
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Cross Validation in R [closed]

Im trying to do a cross validation in R but i don't know where to start from. I have looked online to see if i can find anything but I can't make any sense from it I'm focusing on Premier league data ...
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Lasso cox regression with bootstrap

I'm looking at building a nomogram for cancer prognosis based on 20 variables. This will be derived from a cox ph model. In the past I used poor methodology including dichotomization and stepwise ...
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Practical questions about cluster bootstrap confidence intervals

I want to estimate the accuracy of a machine learning model. I have an independent test set with a vector of trusted labels and a corresponding vector of model-based predictions. If I assume the test ...
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Can you implement Replay Buffers for Reinforcement Learning when most experiences give zero reward?

Specifically, for a deep deterministic policy gradient, DDPG, to expedite the learning speed, it's recommended to use a Replay Buffer What if the reward is only given at a terminal state? Or, most of ...
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Bootstrap resulted in something that looks like a mixed distribution. What do?

TLDR Bootstrapping resulted in a crazy scatterplot. Totally clueless here. I have a dataset (not going to say much about it, it is a bit confidential), running a Markov chain-based algorithm on the ...
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m out of n bootstrap implementation in R

I am wishing to estimate the sampling distribution of an extreme order statistic (the sample maximum). The usual nonparametric (n-out-of-n) bootstrap fails miserably in this case. Chernick (2011) ...
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39 views

Bootstrap confidence intervals do not include the observed mean. Can this be?

I have data on survival and fecundity (fruit production) for a bunch of plants grown in multiple experiments. There are multiple plants per genotype, so I take the trait mean per genotype. I am ...
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Is there an inductive version of a traditional hypothesis test?

Here's my specific question: Is there a statistical procedure that compares a hypothesized value to the empirical distribution, rather comparing an empirical value to a null distribution? Put ...
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General way to construct a confidence interval for a unknown constant to which a sample estimator converges

Assuming that a sample estimator converges to some unknown constant (a wild assumption to be sure) and without assuming the distribution of either the sample estimator or the variables from which it ...
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Bootstrap confidence interval for just-identified IV estimator

Assume we have a regression model \begin{equation} y_{i} = z_{i}' \delta + \epsilon_{i} \end{equation} with dependent variable $y_{i}$, L regressors $z_{i}$ and K instruments $x_{i}$, and assumptions ...
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Ordinary bootstrap preserve rank correlation?

My question is simple: will an ordinary bootstrap preserve rank correlation on the vectors? I.e. I have an m-by-n matrix. M samples of N variables. If I bootstrap, picking M samples uniformly again ...
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Does the size of original dataset influence measurment error in bootstrap? [closed]

As above. So for example would the measurment error of model's r-squared be higher if the bootstrap sample (1000) was drawn from original sample of 20 observation than if the bootstrap sample (1000) ...
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In model or process validation, what's the difference between “bias-corrected bootstrap” and “bootstrap out-of-bag(OOB)”

In Ordinary bootstrap, people draw bootstrap samples from the original sample and fit models using bootstrap samples. Those models are further applied to the original sample to get performance values ...
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How to calculate studentized bootstrap pvalue for H0 assuming % difference between population means?

First of all I'd like to mention, that I've read at least 2 great discussions on the site, which helped me a lot. Very thorough explanations of H0 data generation are presented here and here. But ...
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Bootstrapped linear regression with unbalanced factors

I am investigating the relationship between Valence ratings (continuous response variable) and Condition (4-level factor) as ...
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Imputating variable for Linear Regression

Consider the regression model $Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon$. The data set has $N=20,000$ records. However, the data point $X_{i,2}$, the value of $X_2$ for individual $i$, is ...
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Degrees of freedom in OLS regresison vs Bootstrap

I understand that in OLS, the degrees of freedom for estimating the variance of the residuals is n-q-1. We loose q+1 degrees because they are "used" to analytically determine the q parameters and 1 ...
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Why shift the mean of a bootstrap distribution when conducting a hypothesis test?

I'm wondering about why we do a particular thing (and not another) when conducting bootstrapped hypothesis tests. My understanding of bootstrapped hypothesis tests is this (based on this helpful ...
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Why is bootstrapping called an “optimistic” model validator? When should I use bootstrapping or cross validation?

I understand that k-fold cross validation is a pessimistic model validator because it overestimates generalization error as less data is involved in training sets. Is bootstrapping called "optimistic" ...
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Bootstrap Hypothesis Test: Comparing the Performance of two Models

I have two models $A$ and $B$ as well as a training set $X$. I want to test whether there is a significant difference in performance between model $A$ and $B$. I'm attempting to do this via ...
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Reusing bootstrap weights

I am doing 3 bootstrapping one with 100 replicates, one with 200 replicates, and one with 500 replicates. Is it valid if I generate 500 replicates and use first 100, and 200, and all of them (500) to ...
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72 views

Random forest permutation test: Is permutation of the training set appropriate?

I have a rather high-dimensional data set (p > 1000) with several variables ranking significantly higher than the rest in terms of variable importance (measured by Gini impurity). However, these ...
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42 views

Bootstrap confidence interval of an estimated function

I have a model whose estimation is a function (finite number of points) over an intervalle. I am looking at the sum of each estimated point of the function : $\hat{\theta} := \sum_{i=0}^k \hat{f}(i)$ ...
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Parametric Bootstrap Central limit theorem non i i d

I am having paired data with missing values in a single arm. I am willing to use parametric bootstrap with specific quadratic tests to test the hypothesis of equality of means. My model is as follows:...
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Why does weighted bootstrap have awful coverage even in toy example?

I'm interested in using the weighted bootstrap to correct for selection bias with a known form. I simulated a very simple example where the underlying data, $X$, are $N(0,1)$ and we are calculating a ...
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Random forest - Out-of-bag estimates

I am reading the chapter on random forests by Leo Breiman (found here: https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf). In section 3.1 Using out-of-bag estimates to monitor error, ...
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Calculate Power of Bootstrap Test for Equality of Means

I am new to statistical resampling techniques. Here is a problem I am having difficulty with: I am given two independent Gaussian samples of size $30$ with equal underlying parameters ($mean = 15$ and ...
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Equality of Means (Student, Bootstrap Permutation) Using R

I am getting acquainted with resampling methods. Here is a problem I tried to tackle: I have two normal independent samples of size $60$ of equal variance but possibly different means. The two ...
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Why with probability close to 1 bootstrap and classical tests provide the same decision? Is it caused by loss of pivotality? How?

Here is an example on which my question is based can please someone tell me what is the relation between the probability close to one and the fact that we have same decisions as classical tests and ...
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Bootstrap sampling for ratio of means with uneven sample sizes

I want to obtain a confidence interval for the ratio of means of two samples. The samples are of uneven size. They don't come from normal distributions. Is there anything methodologically wrong about ...
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Does bootstrapping help with power concerns?

I am running a logistic regression, similar to the following: Pr(Y = 1) = B0 + B1*X1 + B2*X2 + B3*X3 + e X1 is an indicator variable. I find B1 is statistically ...
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Finding Null distribution for gbm interactions

I am trying to determine which interactions in a gbm model are significant using the method described in Friedman and Popescu 2008. My gbm is a classification model with 9 different classes. I'm ...
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How to report a bootstrapped regression? Only estimated effects + 95%CI, or more?

I have a beginner bootstrap question. I have a model of which the residuals are non-normally distributed, which cannot be undone by transformation of the DV. I also have multiple IVs, which cannot be ...
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Is bootstrapping a linear mixed-effects model appropriate for (non-independent) time-series data?

I've always been told that "bootstrapping is assumption-free". I don't see how bootstrapping would get around the problem of having auto-correlated observations such as in time-series data. In my ...
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1answer
67 views

Bias corrected calibration curve (regression modelling strategies)

I have a question regarding calibration plot for a binary logistic regression model (calibrate) in the rms(regression modelling strategies) package. The Bias-corrected curve (see below) shows if the ...
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1answer
118 views

Sampling from empirical distribution

I have a vector of y (min is > 0, max could be 1), for which, i have no idea what distribution is. But based on the data we have, vector y, we can get the empirical cumulative probability distribution,...
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Efrons enhanced bootstrap - estimate calibration equation parameters

"The bootstrap method is as follows. From the original X and Y in the sample of size n, draw a sample with replacement also of size n. Derive a model in the bootstrap sample and apply it without ...
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Simulated estimate from a linear mixed model with random intercepts

I wanted to see if there was a quick way to get a bootstrapped parameter estimate and CI using confint() from merTools? ...
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Can we use bootstrap in time series case?

I use random forest for time series forecasting.I have some features: lags. day of year,day of week,hours,minutes. ...
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For what reasons should one use Bootstrap Testing when the sample size is large?

Bootstrap testing is great if we have a small sample size where the Central Limit Theorem does not apply. However, what are convincing reasons we should use Bootstrap if we do have a large sample size....
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Bootstrap Methods - Mathematical Rigour

I'm looking for sources that present an Introduction to Bootstrap Methods in a mathematically rigorous way. I have looked at books such as "An Introduction to the Bootstrap - Efron" and "Bootstrap ...
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arbitrariness in bootstrap bias estimation

The bootstrap estimates bias by applying the "plug-in" principle to $$E(\hat{\theta}_n) - \theta$$ I got this knowledge from p.124 of Efron, Tibshirani, 1994. equation(10.1) $\text{bias}_F=E_F[s(\...