Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [coverage-probability]

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

See https://en.wikipedia.org/wiki/Coverage_probability

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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 can still be a good trade-off because the…
David J. Harris
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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 probability. However, I'm getting something like 94%. …
Him
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Regarding convergence in probability

Let $\{X_n\}_{n\geq 1}$ be a sequence of random variables s.t $X_n \to a$ in probability, where $a>0$ is a fixed constant. I'm trying to show the following: $$\sqrt{X_n} \to \sqrt{a}$$ and $$\frac{a}{X_n}\to 1$$ both in probability. I'm here to see…
Savage Henry
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Is calculating "actual coverage probability" the same thing as calculating a "credible interval"?

I was reading an entry level statistics textbook. In the chapter on maximum likelihood estimation of the success proportion in data with binomial distribution, it gave a formula for calculating a confidence interval and then nonchalantly…
rumtscho
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Posterior variance vs variance of the posterior mean

This question is about the frequentist properties of Bayesian methods. Suppose we have data ${\bf y}$ generated from a distribution with a single parameter $\theta$, equipped with a prior $\pi(\theta)$. This leads to a posterior distribution…
knrumsey
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Random forests confidence intervals and prediction

This is a short simulation to check the coverage of the random forest confidence intervals introduced in the following paper, when used as predictive intervals. S. Wager, T. Hastie and B. Efron. Confidence Intervals for Random Forests: The Jackknife…
Zen
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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 in some information about the distribution and…
BootstrapBill
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Why is the coverage of this lme4 confidence interval less than 95%?

I have data that can be described using the model $y_{i j} = \alpha_i + \epsilon_{i j}$, where $\alpha_i \sim \text{N}(\mu_{\alpha}, \sigma_{\alpha}^2)$ and $\epsilon_{i j} \sim \text{N}(0, \sigma_{\epsilon}^2)$. There are 768 observations in 48…
Victor Verma
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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 $(1-\alpha)\times100$ credible region for $(\theta_1, \theta_2)$. Can anybody…
knrumsey
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coverage index?

Suppose I have a space of potential outcomes X with a probability distribution on it. I assume that there is a distance function between elements of X (e.g. X is a metric space). I also have a set S of points in X. I want to measure how well S…
amit
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convergence in probability for symmetric beta density

I am trying to solve the following problem. Prove that for $X_n\sim \operatorname{Beta}(n,n)$ , $X_n $ converges in probability to $\frac {1}{2}$. This is what I tried: Since as $ n\rightarrow \infty$ , $\mathbb{E} (X_n)\rightarrow \frac {1}{2}$…
ANUJ NAIN
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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, and there are two experimental groups. I am interested in the influence of group on the change from pre to post so the…
Rex Parsons
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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 covariates $\boldsymbol{X} \in \mathbb{R}^p$ and…
Ejrionm
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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 erroneous conclusions would be made?
John Liu
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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/StatisticalModeling/index.html Can anyone explain…
Fawad
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