Questions tagged [coverage-probability]
The probability that a confidence interval actually contains the true parameter.
44
questions
21
votes
2answers
682 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 ...
12
votes
3answers
439 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{...
10
votes
3answers
6k 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 ...
9
votes
1answer
991 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(\...
6
votes
1answer
121 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_{\...
6
votes
0answers
169 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 ...
5
votes
3answers
249 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$ ...
3
votes
2answers
249 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 ...
3
votes
1answer
84 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 \...
3
votes
2answers
83 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 ...
2
votes
2answers
144 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 ...
2
votes
1answer
374 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/...
2
votes
0answers
230 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 ...
2
votes
0answers
151 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 ...
2
votes
0answers
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 ...
1
vote
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, ...
1
vote
1answer
596 views
Calculating the mean excess loss
Suppose $X$ has the following pdf:
$$ f_x(x)=0.01 \qquad for\space 0\le x<100$$
Find the pdf of $X_p$ (the excess-loss variable) and calculate the mean excess loss for $d=10$.
\begin{align}
P(X_p&...
1
vote
1answer
23 views
VaR backtesting: counting the number of rejections
Let's say you calculate the number of VaR rejections for every $r_{1,t}$, $r_{2,t}$,
should you have the same number of rejections in a model, irrespectively of the weights being different?
$[w,\ 1-w]...
1
vote
1answer
46 views
How can I compare the lengths between these two confidence intervals? [closed]
Let $X\sim Beta(\theta,1)$. I was asked to find two confidence intervals and compare their lengths.
The first confidence interval is for $Y=-(logX)^{-1}$ over the set $[y/2,y]$.
The second ...
1
vote
1answer
73 views
Interpretation of values contained in a confidence interval [duplicate]
Are the values within a confidence interval those that do not significantly differ from the point estimate? Or, put differently, how do we interpret the values contained in a CI given that the CI is ...
1
vote
1answer
463 views
Confidence Interval Coverage-error and Type I error
Could somebody explain to me the relationship between coverage error and type one errors in multiple comparisons testing, if there is one in fact? Does a coverage error occur when the true value of ...
1
vote
0answers
47 views
Coverage of the C.I for the variance on a non-normal population
Consider the confidence interval for the population variance $\sigma^2$ constructed under normality: $$\left[A_n,B_n\right]=\left[\frac{(n-1)s^2}{\chi^2_{n-1,\alpha/2}},\frac{(n-1)s^2}{\chi^2_{n-1,1-\...
1
vote
0answers
65 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 ...
1
vote
0answers
256 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.):
...
1
vote
0answers
57 views
Coverage probability and the nominal coverage probability frequently
What is the difference between coverage probability and the nominal coverage probability frequently?
1
vote
0answers
167 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 ...
1
vote
0answers
84 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 ...
1
vote
0answers
74 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 ...
0
votes
1answer
17 views
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 ...
0
votes
1answer
210 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 $91.2$% $...
0
votes
1answer
221 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 ...
0
votes
1answer
302 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 ...
0
votes
0answers
7 views
Difference between coverage probability and confidence coefficient
In the book Casella, G. and R.L. Berger, Statistical Inference, there are two definitions about confidence interval. But they look exactly the same to me. To be more specific about my confusion, in ...
0
votes
1answer
23 views
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:
...
0
votes
0answers
24 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 ...
0
votes
0answers
18 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 ...
0
votes
1answer
88 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 ...
0
votes
0answers
50 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 ...
0
votes
1answer
12 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?
0
votes
1answer
364 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 ...
0
votes
0answers
48 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 $\hat{\mu}$...
0
votes
0answers
323 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 \...
0
votes
1answer
148 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 ...
0
votes
2answers
792 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 ...
