Questions tagged [coverage-probability]

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

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16 views

Double bootstrap coverage failure?

I am working on a simulation to compare different bootstrap algorithms, like normal, percentile, BCa. I also include the double bootstrap or bootstrap-t, which requires a second round of bootstrapping ...
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12 views

How to calculate coverage probability when the true distribution is unknown

I am trying to calculate the coverage probability of my bootstrapping method to know whether the method that I have is valid. However, all that i have is the samples, without knowing the true ...
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39 views

Poor Coverage for Bootstrap Confidence Interval on Mean

Based on a highly skewed population, I was hoping to obtain good coverage with bootstrap (vs standard) confidence intervals. I’m not having much luck. I specify my population in R as a Gamma ...
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1answer
116 views

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_{\...
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1answer
46 views

Interval Estimation for a Binomial Proportion Given a Specific Test Outcome

Imagine that I had a coin, I tossed it 10 times (n) and it came up heads each time (x). What proportion heads I would get if I tossed it infinity times? A point estimate is 100%. I can get the ...
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106 views

How to calculate coverage probability from binomial confidence intervals?

For a given alpha I have been calculating various confidence intervals for a binomial distribution(Wald, Wilson, Agrest-Coulla etc.): ...
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1answer
21 views

VaR backtesting: counting the number of rejections

Let's say you calculate the number of VaR rejections for every $r_{1,t}$, $r_{2,t}$, should you have the same number of rejections in a model, irrespectively of the weights being different? $[w,\ 1-w]...
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1answer
44 views

How can I compare the lengths between these two confidence intervals? [closed]

Let $X\sim Beta(\theta,1)$. I was asked to find two confidence intervals and compare their lengths. The first confidence interval is for $Y=-(logX)^{-1}$ over the set $[y/2,y]$. The second ...
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48 views

Test if confidence interval by observation is correct

I have calculated a "confidence interval" of the days between purchase for 600K users. The exact method I used isn't relevant but a simple version would be for each user calculate the distribution ...
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1answer
11 views

internal process of proc mianalyze procedure [closed]

Does proc mi analyze in sas consider only estimates of imputed values or complete data sets that is imputed values as well as non imputed values?
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10 views

Do confidence interval frequency properties hold across parametric forms?

Say I run 100 entirely different estimation procedures on 100 different datasets and estimate 95% confidence intervals for each (e.g. logistic regression, linear regression, etc.). Purely based on the ...
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45 views

Coverage probability and the nominal coverage probability frequently

What is the difference between coverage probability and the nominal coverage probability frequently?
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1answer
251 views

Coverage probability for Wald confidence interval with small sample size

a) My understanding is that the sample variance (i.e. the squared deviation divided by n - 1 instead of n) constitutes a mean-unbiased estimator of population variance. However, I've run multiple ...
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532 views

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(\...
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44 views

Conditional coverage probability

Suppose I'm interested in a population mean $\mu$ of some finite discrete variable $Y \sim P$ defined on $\mathbb{R}$. I have a $100(1-\alpha)\%$ confidence interval for the sample estimate $\hat{\mu}$...
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2answers
82 views

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 ...
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291 views

Coverage probability for the Bayesian credible interval for Normal distribution

Bayesian Inference for the Normal Distribution, I use the following r code to obtain the posterior distribution. Let's say the data, $X\sim N(\mu, \sigma^{2})$ and $\mu \sim N(0,10)$ and $\sigma \sim \...
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3answers
219 views

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 $(1-\alpha)\times100$ ...
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218 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 ...
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1answer
72 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 ...
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1answer
71 views

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 \...
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156 views

Comparing the results of four missing data imputation methods

Below are the Bias, MSE and Coverage of four missing data imputation methods at different percentages of missing values. From these we can see that, m4 method gives ...
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2answers
141 views

Assessing model prediction performance using tolerance interval coverage

I am trying to assess a model's prediction performance, and one metric I look at is the percentage of new observations that fall within the 95% tolerance interval, and see whether or not it is ...
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1answer
143 views

Number of replications needed for coverage probability study

I am constructing confidence interval based on Wald, likelihood ratio and jackknife for the parameters of a model via simulation. To evaluate which methods is preferable for the parameters, I did a ...
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1answer
2k views

Second order inclusion probabilities in With-Replacement Sampling

I'm reading the book "Model Assisted Survey Sampling" from Särndal et al. In chapter 2, there's a section about Sampling with replacement. I'll put this into context: We have $m$ independent draws, ...
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1answer
181 views

Underestimated Coverage probability

Let $U0$ denotes intercept variance and $U1$ denotes slope variance. Given that the coverage rate for the intercept variance is $91$% $(U0)$ , and the coverage rate for the slope variance is $91.2$% $...
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639 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 ...
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2answers
646 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 ...
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221 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 ...
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3answers
405 views

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{...
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1answer
193 views

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 ...
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0answers
145 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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83 views

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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1answer
578 views

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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71 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 ...
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151 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 ...
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1answer
261 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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1answer
451 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 ...
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1answer
365 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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3answers
5k views

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 ...
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2k views

What exactly is the actual coverage probability? [duplicate]

I am confused about the difference between the nominal and the actual coverage probability. Say we are trying to estimate the fraction of the current population of the US that has been diagnosed with ...