# Questions tagged [bootstrap-sampling]

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

45 questions
Filter by
Sorted by
Tagged with
8 views

62 views

### Sampling from a 2D to 1D distribution

I have one question/problem regarding sampling and I am not sure in which category this falls (it looks like bootstrapping) Let's say that I have some real surface $z = f(x, y)$ on some bounded domain ...
23 views

### Using hypothesis testing to check if a mean of a sample is bigger than the other sample.

Basically I am asked if people over age $35$ spend more money on average than people less or equal to age $35$ with significane level $0.05$. And I have a sample of the population that I can use for ...
29 views

44 views

### What is the limit of $((x-1)/x)^x$ as $x$ goes to infinity?

I came across this limit when considering bootstrapping since $1 - ((x-1)/x)^x$ is the probability that observation $j$ from a sample of size $x$ does appears in a bootstrap sample also of size $x$. ...
59 views

### Probability of a median being $x_i$

I am trying to derive a probability function and here are the assumptions. Let $S = \{x_{(1)},x_{(2)},...,x_{(7)}\}$ be a set of distinct values that are ordered. Let $S*=\{x_1^*,x_2^*,...,x_7^*\}$ ...
25 views

### Relation between bootstrap resampling and $t$-Student test

After scouring the internet and several reference books for a couple of days, I couldn't really find an answer to the current problem I am trying to solve. I have some problem understanding why I can'...
118 views

### How to compute probability of a bootstrap sample

The Question Consider the samples $\{1, 3, 4, 6\}$ from some distribution. a) For one random bootstrap sample, find the probability that the mean is $1$. b) For one random bootstrap sample, find the ...
80 views

80 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 ...
387 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 $n$?
48 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 ...
53 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 ...
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 ...
553 views

276 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 ...
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 ...
30 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
848 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 ...
196 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 ...