Questions tagged [coverage-probability]

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21
votes
2answers
592 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
386 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
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 ...
6
votes
0answers
321 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(\...
5
votes
3answers
205 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 $(1-\alpha)\times100$ ...
4
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0answers
142 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 ...
3
votes
2answers
212 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
67 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
80 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
136 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
353 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
216 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
144 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
1k 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
562 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
20 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
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 ...
1
vote
1answer
71 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
443 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
1answer
31 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 ...
1
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0answers
51 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
36 views

Coverage probability and the nominal coverage probability frequently

What is the difference between coverage probability and the nominal coverage probability frequently?
1
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0answers
148 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
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0answers
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 ...
1
vote
0answers
68 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
173 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
182 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
230 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
47 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
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?
0
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0answers
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 ...
0
votes
1answer
189 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
97 views

How to calculate coverage rates for 95% confidence intervals for estimands (like regression coefficients)?

I'm working on a Synthetic Data Generation model, and I'm confused about a metric mentioned in a seminal paper (details of paper added below) Context: Synthetic Data Generation involves sampling from ...
0
votes
0answers
41 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
272 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
140 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
595 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 ...