Related papers: Interval Estimation of Bounded Variable Means via …
Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We…
Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…
In order to estimate the population mean in the presence of both non-response and measurement errors that are uncorrelated, the paper presents some novel estimators employing ranked set sampling by utilizing auxiliary information.Up to the…
When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…
Prediction intervals are a machine- and human-interpretable way to represent predictive uncertainty in a regression analysis. In this paper, we present a method for generating prediction intervals along with point estimates from an ensemble…
A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we…
This paper introduces an interval state estimation method for discrete-time bounded Jacobian nonlinear systems allying Luenberger-like observer with zonotope set computation. First, a robust observer is designed to obtain bounded-error and…
Measurements are generally collected as unilateral or bilateral data in clinical trials or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…
Prediction intervals in supervised Machine Learning bound the region where the true outputs of new samples may fall. They are necessary in the task of separating reliable predictions of a trained model from near random guesses, minimizing…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
This paper considers the problem of estimating the variance of a sum of a triangular array of random vectors with heterogeneous means. When random vectors exhibit two-way cluster dependence or weak dependence, standard variance estimators…
Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it…
We develop a novel method for counterfactual analysis based on observational data using prediction intervals for units under different exposures. Unlike methods that target heterogeneous or conditional average treatment effects of an…
The estimation of a probability p from repeated Bernoulli trials is considered in this paper. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute…
We show that confidence intervals in a variance component model, with asymptotically correct uniform coverage probability, can be obtained by inverting certain test-statistics based on the score for the restricted likelihood. The results…
In this paper, we establish a fundamental connection between binomial parameters and means of bounded random variables. Such connection finds applications in statistical inference of means of bounded variables.
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
In Part I of this article (Banerjee and Kuchibhotla (2023)), we have introduced a new method to bound the difference in expectations of an average of independent random vector and the limiting Gaussian random vector using level sets. In the…