Related papers: New confidence interval methods for Shannon index
In pharmaceutical and toxicological research, historical control data are increasingly used to validate concurrent control groups, typically via the construction of historical control limits. While methods have been described for continuous…
It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations.…
In this work, we briefly introduce and discuss some of the diversity measures used in Ecology. After a succinct description and analysis of the most relevant ones, we single out the Shannon-Weiner index. We justify why it is the most…
Cross-validation is a widely used technique for evaluating the performance of prediction models, ranging from simple binary classification to complex precision medicine strategies. It helps correct for optimism bias in error estimates,…
When randomized ensemble methods such as bagging and random forests are implemented, a basic question arises: Is the ensemble large enough? In particular, the practitioner desires a rigorous guarantee that a given ensemble will perform…
Given $n=mk$ $iid$ samples from $N(\theta,\sigma^2)$ with $\theta$ and $\sigma^2$ unknown, we have two ways to construct $t$-based confidence intervals for $\theta$. The traditional method is to treat these $n$ samples as $n$ groups and…
Although the methods of bagging and random forests are some of the most widely used prediction methods, relatively little is known about their algorithmic convergence. In particular, there are not many theoretical guarantees for deciding…
We used a metacommunity of 49 discrete communities of aquatic invertebrates to analyze the dynamical relationship between community and metacommunity species distributions as a test of the neutral theory of biodiversity and biogeography. At…
A common feature in many neuroscience datasets is the presence of hierarchical data structures, most commonly recording the activity of multiple neurons in multiple animals across multiple trials. Accordingly, the measurements constituting…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…
Accounting for both rare events and complex sampling presents challenges when quantifying uncertainty for rate estimation in autonomous vehicle performance evaluation. In this paper, we introduce a statistical formulation of this problem…
In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a…
Structural equation models and Bayesian networks have been widely used to study causal relationships between continuous variables. Recently, a non-Gaussian method called LiNGAM was proposed to discover such causal models and has been…
The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to…
While widely used as a general method for uncertainty quantification, the bootstrap method encounters difficulties that raise concerns about its validity in practical applications. This paper introduces a new resampling-based method, termed…
In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a…
The construction of confidence regions for parameter vectors is a difficult problem in the nonparametric setting, particularly when the sample size is not large. The bootstrap has shown promise in solving this problem, but empirical…
Income inequality measures are often used as an indication of economic health. How to obtain reliable confidence intervals for these measures based on sampled data has been studied extensively in recent years. To preserve confidentiality,…