Comparison of Accuracy Properties for Confidence Intervals of the Cross-Product Ratio of Binomial Proportions under Direct-Direct Sampling Scheme

We consider a general problem of the confidence interval for a cross-product ratio ρ=p1(1-p2)/p2(1-p1) according to data from two independent samples. Each sample may be obtained in the framework of direct Binomial sampling scheme. Asymptotic confidence intervals are constructed in accordance with direct Binomial sampling scheme, with parameter estimators demonstrating exponentially decreasing bias. Our goal is to investigate the cases when the normal approximations (which are relatively simple) for estimators of the cross-product ratio are reliable for the construction of confidence intervals. We use the closeness of the confidence coefficient to the nominal confidence level as our main evaluation criterion, and use the Monte-Carlo method to investigate the key probability characteristics of intervals corresponding to direct Binomial sampling schemes. We present estimations of the coverage probability, expectation and standard deviation of interval widths in tables and provide some recommendations for applying each obtained interval.