Linked Questions
13 questions linked to/from What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level?
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Calculate confidence interval for the population variance [duplicate]
Here is the problem:
When cheching the Chi squared distribution table, the it seems like in the solution the denominators should be switched, because for .025 quantile the value is 13.844 and for ....
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Are there any examples where Bayesian credible intervals are obviously inferior to frequentist confidence intervals
A recent question on the difference between confidence and credible intervals led me to start re-reading Edwin Jaynes' article on that topic:
Jaynes, E. T., 1976. `Confidence Intervals vs Bayesian ...
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I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x?
Suppose the 95% confidence interval for $\ln(x)$ is $[l,u]$. Is it true that the 95% CI for $x$ is simply $[e^l, e^u]$?
I have the intuition the answer is yes, because $\ln$ is a continuous function. ...
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Why are confidence intervals of hazard ratios not symmetric?
My understanding is that the confidence interval for a hazard ratio should be symmetrical about the mean (the distance between the lower limit and the mean is the same as the distance between the mean ...
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Highest-density vs equal-tailed confidence interval
When a sampling distribution is symmetric (and I'm okay assuming unimodal too, if necessary), it's natural to center confidence intervals around the point estimate. But for a skewed distribution (e.g. ...
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Asymmetric confidence intervals
Suppose we have iid data $X_i$ with known variance $\sigma^2$, and wish to write an asymptotic $1-\alpha $ coverage CI for the population mean $\mu$. CLT implies that if $z_q$ represents the $q$ ...
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Unable to understand what confidence interval means
I seek to understand what confidence interval is with the aid of following example (which I know how to solve but do not understand the rationale behind it);
Suppose it is known that the weight of ...
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The basic logic of constructing a confidence interval
Consider a model with a parameter of interest, $\theta$, and its point estimator, $\hat\theta$. For simplicity, assume $\hat\theta\sim N(\theta,\sigma^2/n)$ (in numerous instances this could be ...
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Differences between a frequentist and a Bayesian density prediction
What are some essential differences between a frequentist density forecast/prediction and a Bayesian posterior for an outcome of a random variable?
Of course, there will be differences in how they ...
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Interesting question on confidence intervals
Say I conducted a sample and did the relevant processing to get a 95% confidence interval of a parameter to fall between a [10,14].
My friend did another sample, and got a x% confidence interval of a ...
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How can I use this pivotal quantity to find the shortest length confidence interval for $\theta$?
Let $X_1,\cdots,X_n \sim f(x|\theta)=\frac{\theta}{x^2}, x> \theta$ be a random sample where $\theta>0$ is unknown. I want to use $\frac{\theta}{X_{(1)}}$ as a pivotal quantity. How can I use ...
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Confidence Interval for a MOM Estimator of a uniform distribution
If $X$ is a random variable from the uniform distribution on the interval $(\theta, 2\theta)$, how would one construct a 90% confidence interval for the method of moments estimator of $\theta$?
The ...
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Finding the best confidence interval for given confidence level
(This is more of a remark than question, essentially I want to know if there are any works in this direction)
I find method like linear regression unsatisfactory mainly because the prediction for y
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