# Questions tagged [coverage-probability]

The probability that a confidence interval actually contains the true parameter.

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### Conservative coverage probability when an biased estimator is used for the variance

Suppose that $X_n\sim N(\mu, \sigma^2_n)$. Thus, to construct a 95% CI for $\mu$, we can use $X_n\pm 1.96 \sigma_n$. The coverage probability, $P(\mu\in [X_n\pm 1.96 \sigma_n])$, is equal to 95%. ...
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### Random forests confidence intervals and prediction

This is a short simulation to check the coverage, when used as predictive intervals, of the random forest confidence intervals introduced in the paper: S. Wager, T. Hastie and B. Efron. Confidence ...
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37 views

### Small bias but low coverage probability

I tried my codes on 100 and 500 simulation data. Each data has 100, 500, or 1000 observations. The number of simulated data did not affect much of my results. However as I increased the number of ...
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### How to interpret a n-related change in coverage for model (simulation study)

I have repeated measures data from n_subjects where each has n_obs number of measurements before and after some intervention, ...
619 views

### Coverage for confidence intervals

I would like to know if my simulation approach to find the coverage for a confidence interval of a prediction $\boldsymbol{\beta}^T\boldsymbol{X}_N$ is correct I generated a dataset of $n$ samples of ...
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### Not getting 95% coverage for 95% t-distribution CI

I'm simulating a bunch of 95% confidence intervals on samples taken from a normal distribution. Since the data is normal, then, I think, my 95% confidence should translate into a 95% coverage ...
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1 vote
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### What are the implications of a low coverage in multiple imputation?

When testing multiple imputation algorithms in simulations, the bias of the examined estimates and the 95% coverage rate are often used as a quality metric. I understand that it is generally ...
50 views

### Bivariate normal PDF and it's confidence interval coverage

I'im currently studying the confidence interval where the PDF of (X, Y) is a bivariate normal PDF. After calculating the confidence interval, i am calculating the coverage too. Now my question is: ...
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### Confidence Interval of Coverage Probabilities

Does it make much sense to calculate confidence intervals for coverage probabilities? For instance, if a CI coverage probability is estimated to be 0.80, does computing an exact 95% binomial ...
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### Coverage of a Bootstrap Confidence Interval for a Change in a Binomial Proportion

How can I estimate the coverage of a bootstrap confidence interval for a change in a binomial proportion please? For example, if the results from two tests (A and B) are: ...
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1 vote
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### Convergence of Sum of Sums of random variables : trivial?

I have a sequence of i.i.d random varaibles $X_1, X_2, ...$ with finite mean $\mu$ and finite variance. I also have another sequence of i.i.d random varaibles $Y_1, Y_2, ...$ with the same finite mean ...
169 views

### Coverage probability from fiducial/confidence distribution

I am trying to realize how to compute confidence intervals from a fiducial distribution/confidence distribution with possibly more than one parameter. But for now I would just like to understand if I ...
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1 vote
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### Probability distribution of three random variables

The following formula is a formula I got from a paper that deals with wireless networks specifically when calculating coverage probabilities, it is powerful because one can use it for general ...
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### Calculating the mean excess loss

Suppose $X$ has the following pdf: $$f_x(x)=0.01 \qquad for\space 0\le x<100$$ Find the pdf of $X_p$ (the excess-loss variable) and calculate the mean excess loss for $d=10$. \begin{align} P(X_p&...
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1 vote
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### error on truncated rms

I am computing the RMS of a sample to estimate the standar error $\sigma$ of the underlying distribution (for simplicity let say a normal distribution $N[\mu$, $\sigma$]). \$ \text{RMS} = \sum_{i=1}^N ...
366 views

### Why (mathematically) is the parametric bootstrap usually better than the empirical one?

As I know from experience, the parametric bootstrap performs better in terms of coverage probability for confidence intervals then the empirical bootstrap. Of course, this makes sense because you put ...
351 views

### Inconsistency between RMSE and 95% CI Coverage

I am running simulations to compare different weighting methods to estimate the mean of y (with missing values). I use bias, RMSE and 95% CI Coverage as my performance metrics. However, looking at ...
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### Confidence Interval Coverage-error and Type I error

Could somebody explain to me the relationship between coverage error and type one errors in multiple comparisons testing, if there is one in fact? Does a coverage error occur when the true value of ...
419 views

### Why are intervals for means narrower than intervals for individual observations?

I am looking at problem 5.01 relating to Galton's data on adult heights of fathers and sons, from Chapter 5 of Statistical Modelling: A Fresh Approach link to this book: http://www.mosaic-web.org/go/...
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