Questions tagged [bootstrap-sampling]

Use this tag for questions related to a statistical test or metric that relies on random sampling with replacement.

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Statistics - Bootstrap Method

After scouring the internet and reference books for a couple of days I couldn't really find an answer to the current problem I am trying to solve. Lets say that I want to construct a confidence ...
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Bootstrap vs Probability

I recently learned about bootstrap and I am confused with what is the difference between probability density function and bootstrap. For Example: If I consider exponential distribution to find the ...
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12 views

Hypothesis testing with composite populations of unequal size and variance

I am trying to test whether two populations have different means. Let's call the populations "Glaciated" and "Unglaciated." Each population comprises data collected at a number of rivers (9 for ...
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13 views

Calculate the estimator and its standard deviation by Parametric Bootstrap

The third quantile of a distribution function F is the point q such that F(q) = 0.75. Note the q (α; λ) (Gamma distribution). Then, the quantile would be estimated by ^q = q (^α; ^λ). We do ...
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Apply function on two set to create a new (+ process validation: bootstrap iterations)

I am new to algebra and help would be more than welcome to tell me if the process I have built is OK, and if my attempt to apply formula on two sets to create a new one is also OK. Context I have a ...
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1answer
25 views

Apply formula on random sampling without replacement, but with replacement between each iterations

I am looking for an algebraic solution to explain that I apply a formula on a vector constituted of a random sampling of n elements in a population of size N without replacement. The formula is ...
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14 views

Consider why does bootstrap sampling distribution need to compute the estimate, If we knew the true parameters $\theta^∗$?

Page 192 of "Kevin Patrick Murphy. Machine Learning: A Probabilistic Perspective." says The bootstrap is a simple Monte Carlo technique to approximate the sampling distribution. This is ...
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23 views

Is it possible to cluster particles and then resample each cluster?

Is it possible to cluster particles (in the particle filter) and then resample each cluster separately? if yes, the resampling are done parallel?
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13 views

how to understand Bootstrap t - method

Here is the definition of bootstrap t-method in book Statistics and Data Analysis for Financial Engineering with R examples page ...
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22 views

Sampling distribution of a functional T

While studying the bootstrap method, I came across with the following definition of the sampling distribution of a functional T: Let's say $X_1,...,X_n$ are i.i.d with distribution function $F$, then ...
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50 views

Inequality regarding sample mean

I was looking at the book "Asymptotic Theory of statistics and probability, DasGupta A., 2008" and in one point of a proof they use an inequality which I have not been able to understand. Given that $...
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96 views

Expected number of tries to choose x unique values

it's been a long time since I've dealt with probability so I thought I would ask here. I'm sampling elements independently and uniformly and with repetition from a population. Given that the ...
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103 views

Why does bootstrapping approach the distribution of estimator, not mean of the estimator with normal distribution?

The wiki page (https://en.wikipedia.org/wiki/Bootstrapping_(statistics)) sated that bootstrapping allow one to compute and estimate the approximate distribution of the estimator. But why does ...
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78 views

Probabilistic subsampling of an Erdős–Rényi graph

Suppose I have an Erdős–Rényi graph ${\cal G}(n,p)$, where $n$ is the total number of nodes and $p$ is the probability of an edge between any pair of nodes (edges are added independently). I subsample ...
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44 views

Nonparametric Boostrap Confidence Interval For $\text{Var }(\overline X)$

Let $\overline X$ denote the sample mean. If we want to find its variance, we have $\text{var } \overline X = \sigma^2/n$. Now, if we do not have $\sigma^2$ we can instead use: $$\hat \sigma^2 \ \ =...
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62 views

Bootstrap estimate of correlation

I have two sets of observations, the brain size $(x)$ and body size $(y)$ of various animals. I am constructing a bootstrap estimate of the correlation. In order to get the bootstrap estimates, I ...
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271 views

Given a data set of $n$ distinct values, show that the number of distinct bootstrap samples is $(2n-1)$ choose $n$.

Given a data set of $n$ distinct values, what is the proof that the number of distinct bootstrap samples is $(2n-1)$ choose $n$?
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44 views

Finding the expected value of the sum of $x_i^2$

I'm trying to figure out how to prove $$E\!\left(\bar{x} ^2\right) = \frac{1}{n} \sum_{i=0}^n \left(x_i ^2\right)$$ This is for a bootstrap, with no specification as to the distribution. I ...
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2answers
49 views

Probability that an element will not appear in a Sample of size N drawn from a Set of size N with replacement

The probability that an element of a Set A of size N will not appear in a Sample B of size N drawn with replacement from the aforementioned Set A is 1/3 if I am correct. But how can we prove this? I ...
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44 views

How many sets of N elements can we construct by sampling with replacement N elements?

Assuming we have a Set of N elements and we form samples of size N by sampling with replacement the original Set, how many such samples can we construct? Alternatively, the question is: How many ...
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356 views

Intrepretation of Bootstrap method in a simple example, with uniform population to infer.

In order to understand the functionality of bootstrap, i may use a population with uniform distribution to infer. We can generate a sample of 50 points from a uniform distribution $U(0, 1)$ with $\mu=...
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31 views

Test for difference of variances in populations with different means

I have two samples A and B, both of size 72, drawn from two different populations. I do not know anything about the population, only that they are non normal at all. I want to know the probability ...
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420 views

Why is a bootstrap method helping in some way?

The general methods with bootstrapping is always similar to that: We have a given sample $x_1,...,x_n$. Then we pick some elements of the sample randomly and put it then back to the sample; This ...
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2k views

The measure-theoretical definition of a bootstrap sample

I’m currently learning the bootstrap method, and I have two questions to ask about the definition of a bootstrap sample. Let $ (\Omega,\mathscr{S},\mathsf{P}) $ be a probability space. Let $ X_{1},\...
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223 views

Bootstrap method & Confidence Interval

I'm trying to figure out how this method works. My data: 1000 samples from unknown distribution. I need to create 40 vectors from those 1000 samples (each vector with 20 samples) For every one of the ...
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1answer
3k views

How to estimate population mean by bootstrap sampling?

Let's say I have a population of size 1M, and I took a sample of 10k. For each individual of the 10k sample, I recorded an observation x. Afterwords I subsampled the 10k sample 1000 times with ...
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27 views

Parametric bootstrap (Edited)

The first question is quite easy, but I'm stuck with the second one. Any suggestion? http://imgur.com/a/hKmvB
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657 views

SVD: How to scale singular values after rotating U and V (Matlab)

I am very new to linear algebra... I construct a rectangular matrix A1 from some sampled data which is m x n where m > n [U1, S1, V1] = svd(A1) If I then ...
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1answer
157 views

What is meant by Adams Bashforth being a “boot strap” method?

People seem to say that the Adams-Bashforth method requires some "boot strapping" because it needs two initial conditions: $y_{n+1}=y_n+\frac{\Delta t}{2}[3f(t_n,y_n) - f(t_{n-1}, y_{n-1})]$ I ...
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62 views

Why is good to use bootstrapping samples?

I was researching a little about one algorithm called Random Forest, since it use bootstrapping samples, I mean it constructs several samples with replacement from a set, one question came to me, Why ...
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114 views

When is the bootstrap sampling method not applicable?

I have used once the bootstrap sampling method to obtain a confidence interval for the expected daily returns that I had calculated using some data given. As far as I have understood, this method can ...