Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Estimated P-Values In Discrete Models: Asymptotic And Non-Asymptotic Effects, Chris Lloyd
Estimated P-Values In Discrete Models: Asymptotic And Non-Asymptotic Effects, Chris Lloyd
Chris J. Lloyd
The exact null distribution of a P-value typically depends on nuisance parameters unspecified under the null. For discrete models and standard approximate P-values, this dependence can be quite strong. The estimated (or bootstrap) P-value is the exact probability of the P-value being no larger than its observed value, with the null estimate of the nuisance parameter substituted. For continuous models, it is known that such `bootstrap' P-values deviate from uniformity by terms of order m^{-3/2}, where m is a measure of sample size. The main difficulty with discrete models is the breakdown of asymptotics near the boundary. The aim of …
Exact Tests Of Non-Inferiority From Independent Binomial Data Based On Second Order Test Statistics, Chris Lloyd
Exact Tests Of Non-Inferiority From Independent Binomial Data Based On Second Order Test Statistics, Chris Lloyd
Chris J. Lloyd
Recent advances in likelihood asymptotics (Reid, 2003) lead to pivotal quantities that are closer to standard normal than standard pivotals and also respect some kind of conditionality. It is less clear the extent to which these methods work for discrete models. On the other hand, in the context of binomial trials conditional pivotals can lead to more efficient unconditional inferences, see Boschloo (1970) and Lloyd and Moldovan (2007). This suggests that second order pivotals that respect local conditionality might provide more powerful exact tests. For testing the rate ratio from independent binomial samples, we investigate 5 first order pivotals and …