Higher-order approximate confidence intervals

Higher-Order Confidence Intervals for Stochastic Programming using Bootstrapping

We study the problem of constructing confidence intervals for the optimal value of a stochastic programming problem by using bootstrapping. Bootstrapping is a resampling method used in the statistical inference of unknown parameters for which only a small number of samples can be obtained. One such parameter is the optimal value of a stochastic optimization problem involving complex spatio-temp...

Confidence as Higher-Order Uncertainty

With conflicting evidence, a reasoning system derives uncertain conclusions. If the system is open to new evidence, it faces additionally a higher-order uncertainty, because the first-order uncertainty evaluations are uncertain themselves — they can be changed by future evidence. A new measurement, confidence, is introduced for this higher-order uncertainty. It is defined in terms of the amount...

Distribution Free Confidence Intervals for Quantiles Based on Extreme Order Statistics in a Multi-Sampling Plan

Extended Abstract. Let Xi1 ,..., Xini   ,i=1,2,3,....,k  be independent random samples from distribution $F^{alpha_i}$،  i=1,...,k, where F is an absolutely continuous distribution function and $alpha_i>0$ Also, suppose that these samples are independent. Let Mi,ni and  M'i,ni  respectively, denote the maximum and minimum of the ith sa...

Goodness-of-fit and confidence intervals of approximate models

To test whether the model fits the data well, a goodness-of-fit (GOF) test can be used. The chi-square GOF test is often used to test the null hypothesis that a function describes the mean of the data well. The null hypothesis with this test is rejected too often, however, because the nominal significance level (usually 0.05) is exceeded. Alternatively, the level of Hotelling’s test is accurate...

Two-tailed approximate confidence intervals for the ratio of proportions