Related papers: Construction of Confidence Intervals
Interval estimation of quantiles has been treated by many in the literature. However, to the best of our knowledge there has been no consideration for interval estimation when the data are available in grouped format. Motivated by this, we…
We consider a general regression model, without a scale parameter. Our aim is to construct a confidence interval for a scalar parameter of interest $\theta$ that utilizes the uncertain prior information that a distinct scalar parameter…
Large language models (LLMs) excel at numerical estimation but struggle to correctly quantify uncertainty. We study how well LLMs construct confidence intervals around their own answers and find that they are systematically overconfident.…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
AB-testing is a very popular technique in web companies since it makes it possible to accurately predict the impact of a modification with the simplicity of a random split across users. One of the critical aspects of an AB-test is its…
The Negative Binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard Normal approximation often does not provide adequate…
This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but…
Standard random-effects meta-analysis methods perform poorly when applied to few studies only. Such settings however are commonly encountered in practice. It is unclear, whether or to what extent small-sample-size behaviour can be improved…
Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a…
A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is…
Interval estimation of the probability of success in a Binomial model is considered. Zieli\'nski (2018) showed that the confidence interval which uses information about non-homogeneity of the sample is better than the classical one. In the…
The goal of this paper is to develop a practical and general-purpose approach to construct confidence intervals for differentially private parametric estimation. We find that the parametric bootstrap is a simple and effective solution. It…
Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation $\, X \sim {\cal{N}}(\mu , \, \sigma^2) \,$. Here we extend this result to obtaining 1-sample confidence…
Causal inference is crucial for understanding the true impact of interventions, policies, or actions, enabling informed decision-making and providing insights into the underlying mechanisms that shape our world. In this paper, we establish…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and…
This article presents an algorithm that generates a conservative confidence interval of a specified length and coverage probability for the power of a Monte Carlo test (such as a bootstrap or permutation test). It is the first method that…
Bootstrap methods are increasingly accepted as one of the common approaches in constructing confidence intervals in bibliometric studies. Typical bootstrap methods assume that the statistical population is infinite. When the statistical…
In the analysis of survey data it is of interest to estimate and quantify uncertainty about means or totals for each of several non-overlapping subpopulations, or areas. When the sample size for a given area is small, standard confidence…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…