Related papers: The shortest confidence interval for Poisson mean
When searching for new physics effects, collaborations will often wish to publish upper limits and intervals with a lower confidence level than the threshold they would set to claim an excess or a discovery. However, confidence intervals…
Consider a linear regression model with independent and identically normally distributed random errors. Suppose that the parameter of interest is a specified linear combination of the regression parameters. We prove that the usual…
The method of obtaining confidence intervals on a subset of the total number of parameters (p) of a model used for fitting X-ray spectra is to perturb the best-fitting model until, for each parameter, a range is found for which the change…
We derive exact expressions for the shortest path length to a point of a Poisson line Cox process (PLCP) from the typical point of the PLCP and from the typical intersection of the underlying Poisson line process (PLP), restricted to a…
In this article, we study the smallest gaps of the Gaussian orthogonal ensemble. The main result is that the smallest gaps, after normalized by $n$, will tend to a Poisson distribution, and the limiting density of the $k$-th normalized…
We provide a simple method for obtain boundary asymptotics of the Poisson kernel on a domain in $\RR^N$.
We consider the problem of constructing confidence intervals for the median of a response $Y \in \mathbb{R}$ conditional on features $X \in \mathbb{R}^d$ in a situation where we are not willing to make any assumption whatsoever on the…
Robert Cousins has posted a comment on my manuscript on ``Confidence intervals for the Poisson distribution''. His key point is that one should not include in the likelihood non-physical parameter values, even for frequency statistics. This…
Estimating the probability of the binomial distribution is a basic problem, which appears in almost all introductory statistics courses and is performed frequently in various studies. In some cases, the parameter of interest is a difference…
This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signal-independent…
A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any…
This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…
We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.
In this paper, we develop an exact method for computing the minimum coverage probability of Wald interval for estimation of binomial parameters. Similar approach can be used for other type of confidence intervals.
Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are…
The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on…
In this paper, we derive an explicit formula for constructing the confidence interval of binomial parameter with guaranteed coverage probability. The formula overcomes the limitation of normal approximation which is asymptotic in nature and…
Suppose that X_1,X_2,...,X_n are independent and identically Bernoulli(theta) distributed. Also suppose that our aim is to find an exact confidence interval for theta that is the intersection of a 1-\alpha/2 upper confidence interval and a…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
This note points out how confidence interval estimates for standard deviation transform into confidence interval estimates for the power of F-tests at fixed alternative means. An application is shown for the test of a two-sided hypothesis…