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A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
The odds ratio (OR) is a measure of effect size commonly used in observational research. OR reflects statistical association between a binary outcome, such as the presence of a health condition, and a binary predictor, such as an exposure…
For a number of researchers a number of publications for each author is simulated using the zeta distribution and then for each publication a number of citations per publication simulated. Bootstrap confidence intervals indicate that the…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
The empirical Orlicz norm based on a random sample is defined as a natural estimator of the Orlicz norm of a univariate probability distribution. A law of large numbers is derived under minimal assumptions. The latter extends readily to a…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
The standard odds ratio of logistic regression is foundational but limited to individual explanatory variables. This work derives a multivariable odds ratio that applies to all the explanatory variables in all their combinations.
This study aims to evaluate the performance of power in the likelihood ratio test for changepoint detection by bootstrap sampling, and proposes a hypothesis test based on bootstrapped confidence interval lengths. Assuming i.i.d normally…
When we use simulation to evaluate the performance of a stochastic system, the simulation often contains input distributions estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance…
Methods for random-effects meta-analysis require an estimate of the between-study variance, $\tau^2$. The performance of estimators of $\tau^2$ (measured by bias and coverage) affects their usefulness in assessing heterogeneity of…
A decision must often be made between heavy-tailed and Gaussian errors for a regression or a time series model, and the t-distribution is frequently used when it is assumed that the errors are heavy-tailed distributed. The performance of…
A fundamental concept in two-arm non-parametric survival analysis is the comparison of observed versus expected numbers of events on one of the treatment arms (the choice of which arm is arbitrary), where the expectation is taken assuming…
The win ratio is a general method of comparing locations of distributions of two independent, ordinal random variables, and it can be estimated without distributional assumptions. In this paper we provide a unified theory of win ratio…
Our primary aim is to find an estimate of the expected shortfall in various situations: (1) Nonparametric situation, when the probability distribution of the incurred loss is unknown, only satisfying some general conditions. Then, following…
Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an…
Accurately estimating the mixed oil length plays a big role in the economic benefit for oil pipeline network. While various proposed methods have tried to predict the mixed oil length, they often exhibit an extremely high probability…
The logistic regression analysis proposed by Schouten et al. (Stat Med. 1993;12:1733-1745) has been a standard method in current statistical analysis of case-cohort studies, and it enables effective estimation of risk ratio from selected…
The odds ratio (OR) is a widely used measure of the effect size in observational research. ORs reflect statistical association between a binary outcome, such as the presence of a health condition, and a binary predictor, such as an exposure…
For the lognormal distribution, an unbiased estimator of the squared coefficient of variation is derived from the relative ratio of sample arithmetic to harmonic means. Analytical proofs and simulation results are presented.