Tagged Questions

18 views

Calculating sampling bias when estimating population proportions

Assume a true population of size N consisting of red and blue balls, where p represents the frequency of red in the population and q represents the frequency of blue in the population. Let's say that ...
117 views

Estimating population size of a subgroup based on independent samples without replacement

Let a bag have 1000 balls, 100 red and 900 blue. Now, let us get ten independent samples (without replacement within each sample) of the original population (10% each). Proceed to count the number of ...
12 views

Extrapolate a proportion from unequal subsamples

I have a database of species records. Sample X species (number of individuals). Unidentified individuals were classified as "other". In 4% of these samples the category "other" was subsampled ...
78 views

Single sample versus multiple sample

I have a jar with white and black balls. Total number of balls in the jar is 100000. I want to estimate the proportion of white balls. My constraint is that the sample size for estimation should be ...
54 views

Expected maximum given population size, mean, and variance

How would one estimate the maximum given population size, a few moments, and perhaps some additional assumption on the distribution? Something like "I'm going to do $N_s≫1$ measurements out of ...
61 views

Unbiased estimator of variance for samples *without* replacement

This is a follow-up question on that one: Could Bessel's correction make sample variance estimation even more biased? I understand that you need Bessel's correction to get an unbiased estimate of ...
94 views

Could Bessel's correction make sample variance estimation even more biased?

It is well known that Bessel's correction creates an unbiased estimator of variance. What it basically does is divide by $n-1$ instead of $n$. Now what I did is that I chose a few number, like ...
71 views

How should sampling ratios to estimate quantiles change with population size?

I want to cut my data of size N into k equal-sized bins. But I am happy with roughly equal-sized bins, with some $\varepsilon$ error. As precise quantiles of the data are computationally costly ...
107 views

Two-dimensional distribution and related variance computation

I have a simple statistical question (forgive me if I use statistical terminology in a wrong way) Suppose I have a random vector with two components, $(x_1, x_2)$, where $x_1$ can take values from $1$ ...
47 views

Forecast country sales performance based on a subset of areas

It is probably an old and simple problem but I do not have a statistical background and I do not know even how to approach it. The problem is: Given a number of geographical areas in a country (eg: ...
193 views

Estimating values of a sequence from observed differences

I have a sequence of random variables $S_1, S_2 \dots S_N$ that is guaranteed to satisfy $$S_1 + S_2 + \cdots + S_N = 0$$ I can't observe any of these random variables directly, however I can ...
115 views

Bootstrapping Methodology

I have this bootstrap setting: Given $n$ vector-valued statistics (each statistic is a vector) of dimension $r \times 1$, I generated $1000$ bootstrap samples and then generated an estimate of each ...
63 views

Estimating population size and a proportion

I am interested in the following sampling problem, which I will try to describe by a motivating example. Suppose we want to estimate how many people in a certain area, has blue eyes, how many have ...
50 views

Estimating mass proportions from fractional samples

Say you are on a beach that is composed of a mixture of different colored sands (for simplicity, black and white) and you wish to estimate how much there is of each type. You have a bucket that you ...
96 views

Inference on original population based on sample - estimating sampling probability

In my research I am working on some data (let’s call it sales data), however we almost have no information on the original sample. My goal is to come up with possible explanations on how it could be ...
117 views

83 views

Issues when data is unavailable when sampling a finite population without replacement

I am specifying a sample of weekly work records to be entered into a spreadsheet for an estimation of means on two variables. There are about 250 employees, I am only interested in weeks between a ...
77 views

Find the minimum of an expensive-to-sample noisy paraboloid

I have a function on the unit square that's expensive to evaluate, and want to estimate where it reaches its minimum in at most $N$ evaluations, $N$ ~ 10 say. Assuming a model of the form paraboloid + ...
3k views

Why is it claimed that a sample is often more accurate than a census?

When learning the course of sampling, I meet the following two statements: 1) Sampling error leads to mostly variability, nonsampling errors lead to bias. 2) Because of nonsampling error, a sample ...
458 views

Sampling from an unknown distribution

I am using the principle of maximum entropy to fit a density to a given set of samples. I want to generate new set of samples from the approximated density. Is there any way to draw samples from a ...
340 views

How can I estimate unique occurrence counts from a random sampling of data?

Let's say I have a large set of $S$ values which sometimes repeat. I wish to estimate the total number of unique values in the large set. If I take a random sample of $T$ values, and determine that ...
36 views

Calculating/approximating complete Mantel statistic from bootstrap estimates

I have two (sparse) large matrices (~ 1million by 1million) and want to compute Mantel statistic to find correlation between them. To counter memory problems, I have computed the mantel statistic ...
783 views

Acceptance rates for Metropolis-Hastings with uniform candidate distribution

When running the Metropolis-Hastings algorithm with uniform candidate distributions, what is the rationale of having acceptance rates around 20%? My thinking is: once the true (or close to true) ...
265 views

Estimating the variance of poker win rates

Suppose you have a casino with n poker players. Each player has a win rate - the amount of money he wins or loses per hand. We assume that these win rates are normally distributed with a mean of 0. ...
309 views

Nonparametric expected value estimation of sample from unknown distribution

I have a data sample (in this case an EEG data sample, but my question refers to any type of data samples of prior unknown distributions). I would like to do a nonparametric estimate of the expected ...
177 views

Can I estimate the frequency of an event based on random samplings of its occurrence?

Some edits made... This question is just for fun, so if it isn't fun then please feel free to ignore it. I already get a lot of help from this site so I don't want to bite the hand that feeds me. ...