Questions tagged [bootstrap]
The bootstrap is a resampling method to estimate the sampling distribution of a statistic.
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Significant Difference between Confidence Intervals
Supposed I had point estimates over time, with corresponding (95%) confidence intervals for each point estimate (acquired using a parametric-bootstrap), see Figure 1.
I want to determine whether or ...
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28 views
Mean Log10-Linear regression
In field experiment I have gathered data for X and Y with the aim to fit a regression and use X to predict Y in the future. Based on physics, I know the relationship should be of the form
$y = 10^{a \...
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LR test for overlapping return data using bootstrap
I wish to test a null hypothesis as in Christoffersen (1998) to see whether a sequence of Value-at-Risk forecasts $Q_t(p) \in \mathcal{F}_t$ possesses correct conditional coverage. Here $p \in [0,1]$ ...
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Why is sampling 50% of observations in stochastic gradient boosting equivalent to bootstrap sampling?
In the stochastic gradient boosting paper, Friedman (2002) writes that sampling half of the observations before each iteration is "roughly equivalent to drawing bootstrap samples at each ...
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Percentile interval Lemma - proof
Let $\theta$ be a parameter and $\hat{\theta}$ the plug-in estimate, I need a proof of the following lemma, as given in [1], p. 173, in the form of a reference or of a direct argument:
Percentile ...
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Correcting (or bootstrapping) the standard errrors for a two stage glm
Cross posted on StackOverflow
I want to somehow correct the standard errors of my two stage residual inclusion, where in contrast to the 2SLS, the residuals are included in addition to the ...
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15 views
Bootstrap bias-corrected percentiles
Following [1] p. 185-186 the $BC_a$ (bootstrap corrected and accelerated) confidence intervals are given by:
$$
(\hat{\theta}^{*(\alpha_1)},\hat{\theta}^{*(\alpha_2)}),
$$
where $\hat{\theta}^{*(\...
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Leave-one-out cross-validation and stratified bootstrapping together
I had asked a related question related here
I was told that I am using a kind of bootstrapping. I didn't realise it then. Based on the responses, I tried to understand what exactly was going on.
I ...
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37 views
Is bootstrapping redundant for computing confidence intervals for the sample mean in large samples?
If we are just interested in computing confidence intervals for the population mean $\mu$ using a sample $X_1,X_2,\dots,X_n$ of $n$ iid random variables is bootstrapping redundant if $n$ is large?
I ...
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28 views
Sample size is $10^7$, what happens if we bootstrap with replacement using subsample of size $5000$?
Let $\{X_1,X_2,\dots,X_n\}$ be a sample of $n$ iid observations of a random variable $X$, and let $\overline X_n = \frac{1}{n} \sum_{i=1}^n X_i$ be the sample mean.
Now suppose we want to use ...
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20 views
Calculating p-value from bootstrapping procedure
This is a high-level conceptual problem I am facing. I had 5,000 containers that each contain anywhere from a count of 0 - n candies.
I used statistical program to estimate that a particular subset of ...
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Internal validation of BART using bootstrap resampling
I developed a BART model for binary outcome predictions given two numeric independent variables using the pbart R package (v2.9). The code looks like this (sub-setting for 23 observations, complete ...
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1answer
28 views
Bootstrapping mean difference: standard error versus quantiles
I am implementing a bootstrap procedure (in R) to calculate the confidence interval of a difference of two means.
I have little experience with bootstrap but I am ...
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11 views
Reporting p-values for model comparisons (with bootstrap)
I am comparing multiple classification models using several indicators (e.g. Spearman's R, MAE, etc.). I estimated the indicators using a bootstrapped methodology. I then used a simple binomial test ...
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Bootstrapping t-test
Consider two independent random samples x and y with different sample sizes m and n (with m much larger than n).
I wish to:
determine whether the mean of y is significantly different than the mean of ...
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1answer
21 views
Can nested cross validation be considered bootstrapping?
I am using nested cross validation with 5 inner and outer folds. Each of the folds are created using stratified shuffle splits from scikit-learn. Because I am using, can this be considered ...
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Associate uncertainities to variance's estimate of a distribution with heavy tails
I have a set of $M$ variables $\{ \lambda_N^{(i)} \}_{i=0}^{M(N)}$. The distribution of $\lambda$ depends on the $N$ parameter; for $N \rightarrow \infty$ the distribution shrinks around the mean ...
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1answer
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Reference request: accounting for AIC stepwise model selection with bootstrapped standard errors
The use of the AIC for model selection via comparison over many models is well-known and rightly maligned. But I read an interesting passage from Hastie et. al.'s classic The Elements of Statistical ...
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accounting for standard errors when examining correlation between parameters
I have a repeated measures data set with about 100 unique individuals responding (50 responses per individual) that I am using to estimate two different models that each have one parameter. I would ...
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1answer
41 views
p-value equals zero for a bootstrapped sample
Suppose I want to test a null hypothesis that my sample mean $\bar{x}$ equals the parameter $\mu_0$. I perform bootstrapping on my sample and construct a $(1-\alpha)100\%$ confidence interval with the ...
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In bootstrapping, within a single instance of resampling, why do you draw a number of samples equal to your starting N? [duplicate]
I understand that the basic premise of bootstrapping a dataset with N data points is:
Sample with replacement from N a number of draws, D, equal to N;
Repeat step 1 K times - that is, as much as you ...
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KFold CV and Monte-Carlo CV performance for a regression problem
I've ran the following code on google colaboratory. Succintly, I've used some housing prices for a typical regression problem, and then trained the same simple neural network, but with different Cross-...
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Bootstrap for selection among models when best performance is not considered
I understand the title is a bit confusing so I accept any suggestion about it.
I have recently finished reading the book Applied Predictive Modeling by Kuhn and Johnson (you can find more information ...
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1answer
62 views
Bootstrap and normality
I have some problem understanding why I can't just use simple Student's test on bootstrap samples statistic (resample) to find the confidence intervals.
Bootstrap samples statistic should have ...
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Bootstrap estimation of variance and C.I. in cases with small group of outliers
I have a given quantity, say $y_a$ which parametrically depends on $a$ value. I consider $N$ values for the $a$ parameter and, for each one take multiple measures of the corresponding $y_a$ (say $N_a$ ...
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Asymptotics of the maximum of k subsample means
Suppose we have $n$ i.i.d samples $X_1, X_2, \cdots, X_n$ from some real-valued distribution $P$. Let $\alpha \in [0,1]$ be a fixed constant. Select an uniformly random subset $S_1 \subset \{1,2,\...
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1answer
43 views
Hypothesis Testing with a Bootstrap
I have a list of 1000 samples from a distribution. I can find the lower limit of the 95% CI as it is the 2.5% percentile. In this case, it is zero. I would like to also test the hypothesis that a ...
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13 views
Confidence interval for vector of percentages/proportions
How would/should one calculate a 95% confidence interval for the mean of a vector of percentages or proportions?
For example if I had the following vector of percentages, how best would a 95% CI be ...
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32 views
Hypothesis testing after bootstrap
I have a revenue measure over 2 distinct groups of users (group A and B in an A/B test), but the revenue distribution across users is definitely not Normal. In order to measure a random variable that ...
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24 views
Does this Monte Carlo method evidence the consistency of an estimator?
The Statistic
Let $\hat{\theta}(x)$ be a statistical estimator of population parameter $\theta$ whose exact distribution is unknown. Let $\hat{\theta}_n(x)$ be the estimator calculate from a sample of ...
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22 views
Power analysis of mixed model using bootstrapping in R?
I am trying to make power analysis using bootstrap on the following set of data :
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General advice on bootstrapping procedures
This is an open ended question as I am looking for advice and resources. Any suggestions and reference recommendations would help a lot.
I have two datasets, each containing $n$ observations, denoted $...
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1answer
25 views
Coverage of a Bootstrap Confidence Interval for a Change in a Binomial Proportion
How can I estimate the coverage of a bootstrap confidence interval for a change in a binomial proportion please?
For example, if the results from two tests (A and B) are:
...
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SEM with nonnormal data and missings in dataset
I am planning to conduct structural equation modelling and I am confused with all the different ways to handle the following situation:
I have missings on my dependent variable, not on the other ...
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Does this “transpose block bootstrap” make any sense?
Say we have the following data
Say we are concerned with a linear regression model that is $\boldsymbol{y} = \alpha + \boldsymbol{d} \beta + \boldsymbol{u}$ and that we are interested in the ...
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Boostrap Confidence Intervals For 3 Distributions
I am having 3 distributions (A/B/C) and I would like to check if there is any statistical significance difference in their means. The goal is to choose the one with the higher mean if there is a ...
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Why does the bootstrap method work to estimate a statistic? [duplicate]
I am a novice at statistics and recently learned about the bootstrap method. I am curious about why such a method works. Intuitively it feels like we are cheating since we are not collecting new ...
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1answer
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Bootstrap for probability of observing certain data
I am working with years data and I want to see how likely it is for something to have happened for the first time in, say, 1997 given other dates as well. Let me explain.
I have something (a lab ...
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1answer
27 views
Re-sampling with replacement a longitudinal dataset in R
I have a large dataset from a study I conducted in which I'm attempting, for pedagogical reasons, to use for a class. However, due to IRB constraints, I cannot use the real data.
Instead, I would like ...
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1answer
65 views
Jackknifing for assessing the “robustness” of test results
In a presentation I saw recently, a two-sided t-test was repeated with jackknifed subsets of the original data in order to assess the result's "robustness".
In detail, they took a random ...
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34 views
Bootstrapping variance in R gives weird shaped distribution- how to obtain confidence intervals?
this is the first time I've used bootstrapping so it's quite basic!
I'm trying to obtain confidence intervals for the standardised variance- defined as the variance over the square of the mean- across ...
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How to adjust (bootstrapped) confidence intervals for multiple testing in R?
I am comparing effects of different resources by comparing slopes implemented by interaction terms in (generalized) linear mixed effects models e.g. with a negative binomial distribution and a log-...
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36 views
Statistically significant difference in R^2 between two linear regression models
We are interested in if the difference in R^2 between two linear regression models is statistically significant (the metric of model performance doesn't necessarily have to be R^2 but that is what we ...
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1answer
41 views
Estimating population parameter from bootstrapped sample distribution, other than mean value
I'm a rather novice to statistics, so my terminology here might not be totally correct. But I will do my best to explain my question clearly.
My question is about understanding whether it is making ...
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fitting methods for data with bootstrap uncertainities
I have a set of dataset of $N$ couples , say $\{z\}_{i=1}^N$; $z_i = (x_i, y_i)$. The $\{x\}_{i=1}^N$ set has no uncertainities, while the $\{y\}_{i=1}^N$ set has, for each member an uncertainity ...
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Comparison of Coefficients of Variation (CVs)
I have to compare the variability of measures between 2 groups (geographical regions).
Each group consists of a limited number of elements (i.e., the number of districts of each region); hence, a ...
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How can I get p-values (or significance) from bias corrected and accelerated bootstrapping (BCa) in semPLS R?
A similar question has been asked and not yet answered on StackOverflow - someone recommended moving it to here. https://stackoverflow.com/questions/65870669/how-to-get-t-statistics-and-or-p-value-in-...
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1answer
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Is it acceptable to use Boostrap/Jackknife to estimate the variance of an MAP estimators?
Suppose we obtain a point estimate using a maximum a posteriori estimator $\hat{\theta}_{MAP}$. Note that I'm aware Bayesian approaches generally do seek point estimates, but suppose this is an ...
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2answers
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Why does bootstraping not seem to produce a normal distribution for this data?
I am trying to calculate the 95% confidence interval of the mean value of the population. I have this data:
...
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Why subtract the overall mean in bootstrap test for equality of means?
I'm looking at "An introduction to the bootstrap" by Efron and Tibshirani. I'm struggling to understand the procedure they propose:
I don't understand why they subtract the overall mean $\...
