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Questions tagged [coverage-probability]

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Joint credible regions from MCMC draws

Lets say I have $n$ posterior samples of $\theta_1$ and $\theta_2$. I suppose that any region $R$ which contains exactly $(1-\alpha)n$ of the points will be an approximate $(1-\alpha)\times100$ ...
179 views

Econometrics: What will happen if I have a biased estimator (either positively or negatively biased) when constructing the confidence interval

Suppose that the OLS estimator for $\beta_j$ is in fact biased. How would this affect the use of confidence intervals as hypothesis testing tools (assuming a two-tailed test)? That is, what sort of ...
62 views

Interpretation of values contained in a confidence interval [duplicate]

Are the values within a confidence interval those that do not significantly differ from the point estimate? Or, put differently, how do we interpret the values contained in a CI given that the CI is ...
56 views

510 views

confidence intervals' coverage with regularized estimates

Suppose I'm trying to estimate a large number of parameters from some high-dimensional data, using some kind of regularized estimates. The regularizer introduces some bias into the estimates, but it ...
395 views

coverage of confidence interval

I need to check the coverage of a confidence interval, but I don't know which one of the following approaches I should use. Approach 1: Estimate the regression parameter $\theta$ Use the sandwich ...
179 views

Confidence Intervals of a Given Width

I'm working through some questions on confidence intervals. My answer doesn't match the book, but the book's answer was a number I had a few steps before the end. I have ten numbers which are a ...
342 views

64 views

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 ...
130 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 ...
182 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 ...
419 views

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 ...
296 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/...