All Questions
Tagged with confidence-interval variance
110
questions
28
votes
3
answers
4k
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Confidence Interval for variance given one observation
This is a problem from the "7th Kolmogorov Student Olympiad in Probability Theory":
Given one observation $X$ from a $\operatorname{Normal}(\mu,\sigma^2)$ distribution with both parameters unknown, ...
- 4,279
23
votes
1
answer
43k
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Why is chi square used when creating a confidence interval for the variance?
This is a very basic question. Why do we use a chi square distribution? What is the meaning of this distribution?
Why is this the distribution used for creating a confidence interval for the variance? ...
- 675
12
votes
2
answers
3k
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How can I pool bootstrapped p-values across multiply imputed data sets?
I am concerned with the problem that I would like to bootstrap the p-value for an estimate of $\theta$ from multiply imputed (MI) data, but that it is unclear to me how to combine the p-values across ...
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10
votes
3
answers
715
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How to get confidence interval for the population variance?
I have data that is reasonably assumed to be iid samples from some distribution. Our goal is to put a confidence interval on the population variance. Notationally, we have IID $X_i, i = 1, ..., n$ ...
- 483
9
votes
4
answers
3k
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Would a $(1-\alpha)100\%$ confidence interval for the variance be narrower if we knew the mean a-priori?
Let's say we know the mean of a given distribution. Does this affect the interval estimate of the variance of a random variable (which is otherwise computed using the sample variance)? As in, can we ...
- 193
8
votes
1
answer
932
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Are group effects in a mixed effects model assumed to have been picked from a normal distribution?
Say we're interested in how student exam grades are affected by the number of hours that those students study. We sample students from several different schools. We run the following mixed effects ...
- 14.5k
8
votes
1
answer
483
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Can I use a confidence interval of poisson mean for its variance
In a Poisson distribution the mean equals the variance. I would like to find a confidence interval of the variance. Is my reasoning below correct?
Using the central limit theorem I construct a 95% ...
- 4,079
7
votes
2
answers
2k
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Using bootstrap for glm coefficients variance estimation (in R)
I am fitting a GLM model (in R), and would like to get an estimation of the variability of the coefficients estimated by the model.
If I understand it correctly the method to use in such a case is ...
- 21.8k
6
votes
3
answers
5k
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95% confidence interval for a given data set
I have a data set $\mathcal{S}$, which is univariate. I would like to discover the data points which can be thought of as outliers of $\mathcal{S}$. I use $\bar{\mathcal{S}}+2*\sigma(\mathcal{S})$ ...
- 5,222
6
votes
2
answers
3k
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Putting a confidence interval on the mean of a very rare event
I'm simulating an extremely rare event (the detection of weighted photon packets in a highly absorbing material). For example, I may simulate the transmission of 1e9 photons and only detect 10 of them ...
- 373
6
votes
1
answer
146
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Error bars on log of big numbers
I am calculating a quantity of the following form:
$\mu = \log( \frac{1}{n} \sum_{i=1}^{n} e^{\phi(X_i)} )$
via MC. $X_i$ are iid and I can sample them. I want to give error bars\ confidence ...
- 2,634
5
votes
2
answers
519
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Understanding the role of the chi-squared distribution in the confidence interval for the variance
In my textbook they have this inequality:
$$ \chi_{1-\frac{\alpha}{2}}^2 < \frac{(n-1)s^2}{\sigma^2} < \chi_{\frac{\alpha}{2}}^2$$
which later becomes this statement:
$$\frac{(n-1)s^2}{\chi_{\...
- 61
5
votes
1
answer
1k
views
Variance of unbiased estimator for the shape parameter of Pareto distribution
I'm interested in getting the error bounds of the unbiased estimator of the shape parameter ($\alpha$) using maximum likelihood method of Pareto distribution.
The unbiased estimator is known to be
...
5
votes
1
answer
45
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In Regression Through the Origin, why do the CIs of the slope depend on datapoints with zero x value?
I'm working with a Regression Through the Origin model as described in this reference.
The model is $Y_i = \beta X_i + \epsilon$ and the least squares estimate of $\beta$ is $\hat\beta = \frac{\sum ...
- 151
5
votes
1
answer
9k
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Confidence interval for the standard deviation on a bimodal distribution
I have a bimodal distribution, and I wish to estimate the mean and standard deviation of the population (well, these could be 2 sub-populations according to the shape).
With the mean I have no ...
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