Questions tagged [bootstrap]

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

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Bootstrapping t-statistics order of approximation error

Consider bootstrapping the $t$-statistics: $T_n = T(X_1,...,X_n) = \sqrt{n-1}\frac{\bar{X} - \mu}{\hat{\sigma}}$ for iid observations $(X_1,...X_n)$, where $\bar{X} = \frac{1}{n}\sum_{i=1}^{n}X_i$ and ...
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Stationary Bootstrap Block Size Impact on Portfolio Simulation Results

I'm analyzing simulated portfolios generated using the stationary bootstrap method proposed by Politis et al. (1994). This method is expected to be robust to the choice of average block size, as it ...
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Testing for statistical significance between two dependent (unpaired) groups

I'm currently conducting some research on inflation perceptions and I have two groups of data (Group 1 with 67 responses, Group 2 with 71 responses). Group 1 were asked question x, and Group 2 asked ...
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Does the Law of Large Numbers work better for some Distributions? [closed]

Here are two popular principles in Statistics: 1) Law of Large Numbers: If $X$ is a random variable with a probability density function $f(x)$ and an expected value $E[X] = \mu$. If we take a sample ...
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Running Bootstrapping on GAMLSS [closed]

I'm trying to evaluate my model's performance using bootstrapping and this is the function I'm using: ...
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Does Bootstrapping Overcome Limitations in Estimations?

Part 1: Suppose we have some sample data (univariate). We believe that this data came from a Normal Distribution. Using MLE, we can show that the mean estimator will be unbiased but the variance ...
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Proof of property of Mallows/Wasserstein metric

Let $\mathcal F_p=\{H\text{ is a cumulative distribution function}:\int|x|^pdH<\infty\}$. Define on $\mathcal F_p,$ Mallows' metric ($p$ Wasserstein metric), $d_p,p\ge1$ for two random variables $X,...
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Estimating Standard Error of the Mean Across Multiple Samples: Method Selection and Best Practices

I have multiple samples, each of size (n), and I'm exploring different methods to estimate the Standard Error (SE) of the mean. I understand there are several approaches, but I'm seeking insights into ...
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Stratified boostrap for stratified experiment

I'm running an AB test where I split customers into A and B by stratifiying on the levels of a variable X. I collect data like this: ...
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Comparison of confidence intervals: bootstrap & exact resampling

Consider data $X_1,...X_n$ generated from a probability distribution $F$ with density $f$. I'm interested in constructing confidence intervals for a parameter say, $\theta(F)$. Via Monte Carlo ...
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Determining number of repeat measures needed to deal with measurement error through bootstrapping?

I have a performance test with a high degree of inherent measurement error. I have some data from a pilot study where I took 30 repeat measures with a single device and I want to figure out how many ...
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Bootstrap comparison of means

I want to compare means between two groups using bootstrapping, where the groups are represented as separate columns in a data frame. The implementation below works, but the bootstrap comparison is a ...
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How to diagnose the number of bootstraps I need?

I am running an XGBoost model to predict the global economic cost of invasive species. My training set is only about 3000 data points. I am bootstrapping my predictions, and went with the default 1000 ...
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Growth Curve Model with time-invariant covariates- standardized CIs

I ran a growth curve model (GCM) with covariates and used the 95% bootstrapping CIs to interpret the effects of the covariates on the intercept and slopes. I noticed that the upper bound of the CI of ...
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Using bootstrap to compare performance of two machine learning models

I have a binary classification problem, and two ML models $A$ and $B$. I evaluate performance of these models using the area under the ROC curve (AUROC). I want to assess whether model $A$ is ...
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p-values from CIs?

Is there a way to calculate p-values from bootstrapped CIs extracted with the quantile function? ...
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Can bootstrap adjustment for $p$-value in AR model be applied to distributed lag model?

In Wang "Multiple testing correction in time series: rolling window analysis with applications of GWAS methods" (2022), the author mentioned that bootstrap minimum $p$-value can be applied ...
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What is the best way to calculate confidence interval for spearman correlation by bootstrapping? [closed]

I find important differences for the confidence interval values between the two methods below with bootstrap : First : quantile(Rs, prob=c(0.025, 0.975)) and Second : tanh(atanh(R) ± 1.96 sqrt(n-3)) (...
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Does Bootstrapping the Test Set Provide a Real Error Confidence Interval?

My question here is a specific example of what was discussed in part in the answers of Bootstrapping test set? . Suppose I train a model where I cannot mathematically derive a confidence interval for ...
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Probability mass function of sample median (Bootstrap)

Consider a sample $X_1,X_2,...X_n\overset{\text{iid}}{\sim}F$. Let $T_n=F_n^{-1}(1/2)$ be the sample median where, $F^{-1}(x)=\inf\{t:F(t)\ge x\}$ and $F_n(y)=\frac{1}{n}\sum_{i=1}^n\mathbb{I}(X_i\le ...
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If bootstrap works for $\hat{\alpha}$ and for $\hat{\beta}$, does it work for $\widehat{\alpha\beta}$?

Let $\textbf{X}_1, \dots, \textbf{X}_n$ be an (iid) random sample. From this random sample, we compute $\hat{\alpha}$ (an estimation of a certain parameter $\alpha$). Let $\textbf{Y}_1, \dots, \textbf{...
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Bootstrapping moderately extreme quantile regression

Let $(Y_1, X_1), \dots, (Y_n, X_n)$ be iid sequence drawn from $F$. For a fixed $q\in (0,1)$, consider the linear q-quantile regression $Q_Y(q|x) = \beta_qx$, where $Q_Y(\cdot\mid x)$ is the ...
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Explanation for the success of bagging

I'm reading Machine Learning - A First Course for Engineers and Scientists. On page 168 they give a rough explanation for why bagging works. I'm a little confused by their explanation. They consider ...
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Bootstrap confidence intervals: proving correctness

I am working on using a bootstrap technique to compute confidence intervals of a parameter of interest. Let $\textbf{Z}_1, ... \textbf{Z}_n\in\mathbb{R}^d$ be an (iid) random sample. From this random ...
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Valid confidence intervals for AUC with very few cases?

Situation: I have a data set of patients who are positive for a certain illness. I also have a score for 1-year mortality from this illness, designed using a separate data set. The plan is to check ...
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What is the hypothesis test I've used, or what should I change to fit a "common" one?

I've had discussions with several professors, as well as scouring the internet (and chatgpt), trying to improve the description of the methods I've used, or to look for better ones. I'm hoping a wider ...
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Confidence interval for non i.i.d. sample

I'm facing this machine learning problem in real life, that turns to stem from a statistics problem. Given a test set S of size N samples with a statistic x (x is the mean accuracy across the N ...
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Block size in subsampling and bootstrap for time series

I have a dependent variable, a time series of 80 periods (discrete decisions). I am doing maximum likelihood estimation with 10 parameters. Now I want to get the standard error or confidence interval ...
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How to perform inference in a simple mediation analysis?

I am running a very simple version of a mediation analysis with five variables, $y, x, t, z1, z2$. It's simple in that I am only including the mediated effect. I first run $y = x + t + e1$. Next, I ...
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Bootstrapping subsampling analysis

I am currently working on a bootstrapping subsampling analysis, aiming to match a dyslexia group with a comparison group based on their reading achievement scores using PSAboot: Bootstrapping for ...
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Poisson Percentile Bootstrap Intervals

In Efron and Hastie's Computer Age Statistical Inference, they consider the problem of deriving confidence intervals for an estimated Poisson parameter. $\hat{\theta}=10$, where $\hat{\theta}\sim Pois(...
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What to do when my sample size is small to demonstrate an equivalence study

I'm analyzing data from a study comparing 5 treatment arms. Women receiving ovarian stimulation for in vitro fertilization at different phases of the ovarian cycle. The treatment efficacy endpoint was ...
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Nonparametric way to perform ANOVA of linear mixed model for small sample and power calculation

I have a small data where there are 3 groups (A,B,C) and 5 participants from each group. All of those participants are measured 6 times on each of 7 different exams, so each participant get 6*7=42 ...
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Can I remove a single bootstrap sample before calculating CI?

I'm using boot::boot with BCa to assess uncertainty estimation for a binomial model. The statistic function is manually coded as a cluster bootstrap with G-...
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Fitting uncertainty vs. bootstrap uncertainty

I'm currently working with some power law data of the form: $Y_i = \beta \times X_i ^{-\gamma} $ Where $Y_i$ are my measurements at point $X_i$. The uncertainty on $X_i$ is vanishingly small and can ...
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Disagreement in bootstrapping confidence interval and p values (PROCESS conditinal direct effect)

I constructed a moderated mediation model (PROCESS Model 8). Bootstrap results for regression model parameters showed that the BootCI for the interaction term included zero, but in the model summary, ...
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Variance of a bootstrap sample mean

I need help with calculating the variance of a bootstrap sample mean. I want to answer the following question (question 15.4 in The Elements of Statistical Learning). Suppose $x_i$, $i=1, \ldots , N$ ...
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When doing bootstrapping, can you take smaller samples of a sample with replacement?

For example, can I take samples of size ten with replacement from a sample of size 100? I'm trying to teach my high school statistics students about bootstrapping and I want to use m and ms candy, but ...
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How can Bootstrapping explain the uncertainty of a statistic?

I have been reading about bootstrapping, and sampling distributions, and find it odd that people use these techniques to describe uncertainty. As I understand it, the sampling distribution shows ...
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What do you do when bootstrap sample gives a numerically "bad" set of samples?

What do you do when bootstrapping and the sample for one iteration is "bad" in some way that makes your statistic uncomputable. For example suppose your statistic was the best fit linear ...
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CoxPH with one ID contributing many comparator observations

UPDATE----------------- I have data where one ID can serve as a comparator several times. This is done by creating a variable to group the treated in variable GROUP....
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Which statistical test is appropriate to compare two parametric bootstrap samples drawn from model fits of two time series?

In previous threads , parametric bootstrapping was suggested as a method to test for differences between time series at specific time points. I have followed the methods as described in this answer (...
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How to compare metrices in terms of RELATIVE bootstrap confidence interval

Situation: We are assessing several metrices to compare two distributions (e.g. ttest-pvalue, Wasserstein distance, binary classification metrices like ROC-AUC, etc.). One criteria should be the "...
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What maximum value of AUC optimism could still be allowed to confirm that logistic regression model does not overfit?

I am not sure how to define that a statistical model does not overfit based on a difference between bootstrapped AUC and AUC calculated on all training data. In the literature I saw 2 approches. The ...
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Why does my bootstrap sampling distribution no resemble the true sampling distribution?

In trying to understand the bootstrap method, I have taken a sample of 11 observations from a Poisson distribution with a mean of two. I have obtained the following sample: Assuming I do not know the ...
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What standard error should I use with correlated clusters in maximum likelihood estimation of multinomial logit

I have a dataset with 14 clusters. Each cluster is a time series of 80 periods with autocorrealtion, and I am doing maximum likelihood estimation of a structural multinomial logit model. I suspect ...
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One off the advantages of the bootstrap is that i don't have to worry about having a good estimator?

I'm learning about the theory of estimators and saw that sometimes the analytical formula of the estimator has to be diferent off the formula for the parameter, for example the standart deviation, and ...
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Reporting internal validation from .632 bootstrap in caret

I am developing Machine learning prediction models using the caret package in r (Elastic net, SVM, Random Forest, XGBoost). I have 650 cases with 104 having the event of interest. Instead of splitting ...
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Distribution of a bootstrap sample from a given reference sample [duplicate]

Consider $n$ samples $X_1,X_2,..,X_n$, where each is normally distributed according to mean $\mu$ and variance $\sigma^2$. We use these samples to define our reference population. Given a bootstrap ...
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Are bootstrapped samples considered to be coming from the same distribution as the original sample?

Let a dataset $\mathcal{D}$ be sampled according to $F_{\mathcal{D}}$. My question is, suppose I create bootstrapped samples from $\mathcal{D}$. That is, create $\mathcal{D}_1, \ldots, \mathcal{D}_M$ ...
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