Constructing binomial confidence intervals with near nominal coverage by adding a single imaginary failure or success

2006 ◽  
Vol 25 (21) ◽  
pp. 3679-3695 ◽  
Author(s):  
Craig B. Borkowf
Keyword(s):  
Confidence Intervals ◽  
Nominal Coverage

scholarly journals Bootstrap Methods in Econometrics

2019 ◽  
Vol 11 (1) ◽  
pp. 193-224 ◽  
Author(s):  
Joel L. Horowitz
Keyword(s):  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Test Statistic ◽  
Bootstrap Methods ◽  
First Order ◽  
Coverage Probabilities ◽  
Asymptotic Distribution Theory ◽  
Nominal Coverage ◽  
Distributional Approximations ◽  
Approximations To Distributions

The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap provides approximations to distributions of statistics, coverage probabilities of confidence intervals, and rejection probabilities of hypothesis tests that are more accurate than the approximations of first-order asymptotic distribution theory. The reductions in the differences between true and nominal coverage or rejection probabilities can be very large. In addition, the bootstrap provides a way to carry out inference in certain settings where obtaining analytic distributional approximations is difficult or impossible. This article explains the usefulness and limitations of the bootstrap in contexts of interest in econometrics. The presentation is informal and expository. It provides an intuitive understanding of how the bootstrap works. Mathematical details are available in the references that are cited.

scholarly journals Phylogenetic multilevel meta-analysis: A simulation study on the importance of modeling the phylogeny

2020 ◽  
Author(s):  
Ozan Cinar ◽  
Shinichi Nakagawa ◽  
Wolfgang Viechtbauer
Keyword(s):  
Confidence Intervals ◽  
Simulation Study ◽  
Variance Component ◽  
Meta Analysis ◽  
Analysis Model ◽  
Multilevel Structure ◽  
Nominal Coverage ◽  
Multiple Species ◽  
Meta Analyses ◽  
Coverage Rates

Meta-analyses in ecology and evolution typically include multiple estimates from the same study and based on multiple species. The resulting dependencies in the data can be addressed by using a phylogenetic multilevel meta-analysis model. However, the complexity of the model poses challenges for accurately estimating model parameter. We therefore carried out a simulation study to investigate the performance of models with different degrees of complexities. While the overall mean was estimated with little to no bias irrespective of the model, only the model that accounted for the multilevel structure and that incorporates both a non-phylogenetic and a phylogenetic variance component provided confidence intervals with approximately nominal coverage rates. We therefore suggest that meta-analysts in ecology and evolution use the phylogenetic multilevel meta-analysis model as the de facto standard when analyzing multi-species datasets.

scholarly journals A coverage probability of bootstrap-t confidence interval for the variance

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2967-2974
Author(s):  
Vesna Rajic
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Edgeworth Expansion ◽  
Square Root ◽  
Population Variance ◽  
Data Set ◽  
Unknown Variance ◽  
Nominal Coverage

We examine one-sided confidence intervals for the population variance, based on the ordinary t-statistics. We derive an unconditional coverage probability of the bootstrap-t interval for unknown variance. For that purpose, we find an Edgeworth expansion of the distribution of t-statistic to an order n-2. We can see that a number of simulation, B, has the influence on coverage probability of the confidence interval for the variance. If B equals sample size then coverage probability and its limit (when B ? ?) disagree at the level O(n-2). If we want that nominal coverage probability of the interval would be equal to ?, then coverage probability and its limit agree to order n-3/2 if B is of larger order than the square root of the sample size. We present a modeling application in insurance property, where the purpose of analysis is to measure variability of a data set.

A problem with confidence intervals.

1995 ◽  
Vol 50 (12) ◽  
pp. 1102-1103 ◽  
Author(s):  
Robert W. Frick
Keyword(s):  
Confidence Intervals

A Note on Confidence Intervals and Model Specification

Marketing ZFP ◽  
2019 ◽  
Vol 41 (4) ◽  
pp. 33-42
Author(s):  
Thomas Otter
Keyword(s):  
Confidence Intervals ◽  
Generalized Linear Model ◽  
Statistical Information ◽  
Regression Coefficients ◽  
Model Specification ◽  
Model Parameters ◽  
Exploratory Research ◽  
Empirical Calibration ◽  
Credible Intervals ◽  
Model Structures

Empirical research in marketing often is, at least in parts, exploratory. The goal of exploratory research, by definition, extends beyond the empirical calibration of parameters in well established models and includes the empirical assessment of different model specifications. In this context researchers often rely on the statistical information about parameters in a given model to learn about likely model structures. An example is the search for the 'true' set of covariates in a regression model based on confidence intervals of regression coefficients. The purpose of this paper is to illustrate and compare different measures of statistical information about model parameters in the context of a generalized linear model: classical confidence intervals, bootstrapped confidence intervals, and Bayesian posterior credible intervals from a model that adapts its dimensionality as a function of the information in the data. I find that inference from the adaptive Bayesian model dominates that based on classical and bootstrapped intervals in a given model.

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