All Questions
Tagged with estimators sampling
23
questions
3
votes
0
answers
57
views
What is a measure of hardness-of-approximation by samples?
Suppose there is a large vector $\mathbf{x}$ of real numbers, and I want to estimate a certain aggregate function $f(\mathbf{x})$ by taking a small sample of the population $\mathbf{x}$. I would like ...
- 1,029
3
votes
0
answers
25
views
How to illustrate the validity of bootstrap with monte carlo simulation?
Suppose I have a random sample $S_n=\{W_i\}_{i=1}^n$ where $W_i\sim F $, and I have an estimator $\widehat{\beta}$ computed using this sample. I want to illustrate that the bootstrap approximation ...
- 2,966
3
votes
2
answers
560
views
Confusion about the notation in Horvitz-Thompson estimator
I am a bit confused about the terminology used in the context of sampling of populations. The Horvitz-Thompson estimator, as well as the Hansen-Hurwitz estimator, for example, are examples of ...
- 33
4
votes
3
answers
163
views
When can we get unbiased estimate given biased data?
There was a recent "hot take" tweet by Andrej Karpathy (without any comment or clarification from the author):
real-world data distribution is ~N(0,1)
good dataset is ~U(-2,2)
It provoked ...
- 140k
0
votes
1
answer
133
views
Inverse transform sampling : comparing bias, variance and mse for an estimator
Starting from the PDF of the Pareto distribution,
\begin{equation}
f_{\theta_1, \theta_2}(x) =
\begin{cases}
\frac{\theta_1 \theta_2^{\theta_1}}{x^{\theta_1 + 1}}, &\quad x \geq \theta_2 \...
- 111
2
votes
1
answer
460
views
When is subsetting survey data prior to analysis NOT a problem?
Survey researchers are typically advised to not subset their data prior to analysis because it will produce incorrect variance estimates. My understanding of the inferential issue is that removing ...
- 847
8
votes
4
answers
632
views
How to estimate $P(x\le0)$ from $n$ samples of $x$?
Suppose, we have $n$ samples $x_i$ of a random variable:
$$x \sim \mathcal N(\mu,\sigma^2) $$
Based on the samples, we want to estimate the probability that $x$ is negative:
$$P(x\le0)$$
Intuitively, ...
- 1,230
1
vote
0
answers
389
views
How to weight samples in a subsample of a stratified sample?
Suppose I'm first interested in computing the percentage of people in a certain town with brown eyes. However, due to some constraints I end up with the following stratified sampling set up:
$$N = ...
- 51
2
votes
2
answers
110
views
Variance derivation for estimator
I am working to try to determine the variance for the following specific situation:
I have a seed trap where I collect and weight a total amount of seeds, I call this seed biomass. I measure the seed ...
- 33
2
votes
0
answers
83
views
Using variance of sample to calculate unbiased estimate of population variance
I am trying to follow through the survey sampling chapter of Rice's statistics book.
Denote the sample values by $X_1, X_2, \ldots, X_n$ and the population values by $x_1, x_2, \ldots, x_N$ (so the ...
- 356
0
votes
1
answer
89
views
Unbiased estimatior for $\bar{x} $ from a Random Sample with unequal selection probability
I have the following population:
Where the left column is the age of our individuals and the right column is their weight (in kg).
The exercise tells us that we use Random Sampling with no ...
- 23
1
vote
0
answers
33
views
More efficient estimator in this situation?
I am thinking about the following situation (it is an example):
There are N families in a city and we have a simple random sample of size n. In that sample we know that there are $x_{0}$ families with ...
1
vote
0
answers
81
views
Expectation of Sample Variance
This is a question from the book Casella and Berger:
where $ES$ actually means $\mathbb{E}(S)$ (expectation of S)
So, I manage to use the Jensen Inequality to prove that $\mathbb{E}(S) \leq \sigma$,...
- 373
1
vote
1
answer
66
views
Expected value without complete sample space
The book way:
Suppose, we have a bag with 8 balls numbered 1-8, we want to estimate the population parameter mean. we note down the entire sample space. (1,1)(1,2).. (8,8) calculate mean of each ...
- 77
3
votes
0
answers
172
views
Confusion in terminologies for simple linear regression model [closed]
Please go through my draft summary below and let me know if my conventions are correct, comprehensible, and non ambiguous.
Simple Linear Regression Model
Let given observed sample set be $\{(x_1,...
