國立政治大學統計學系主講人：Prof. Andrei Volodine
學 術 演 講
學 術 演 講
Department of Mathematics and Statistics, University of Regina, Canada
題 目：Confidence intervals for the cross-product ratio of binomial proportions under
different sampling schemes
時 間：民國112年5月2日 (星期二) 下午3：00
We consider a general problem of the interval estimation for a cross-product ratio according to data from two independent samples. Each sample may be obtained in the framework of direct or inverse binomial sampling schemes. Asymptotic confidence intervals for the cross-product ratio of binomial proportions are constructed in accordance with different types of sampling schemes, with parameter estimators demonstrating exponentially decreasing bias.
Our goal is to investigate the cases when the relatively simple normal approximations for estimators of the cross-product ratio are reliable for constructing linear and logarithmic confidence intervals. We use closeness of confidence coefficient to nominal confidence level as the main evaluation criterion. Additionally, the Monte Carlo method is employed to investigate key probability characteristics of intervals corresponding to all possible combinations of sampling schemes. We present estimations of coverage probability, expected length, and standard deviation of interval lengths. Simulation results show that the proposed linear confidence intervals possess quite low precision and poor accuracy properties. On the other hand, these logarithmic confidence intervals perform well in terms of coverage probability in many cases and show much better precision and accuracy properties. In addition, we offer recommendations for applying each interval obtained. Proposed confidence intervals were applied to real data applications for all four sampling schemes.
Keywords: Cross-product ratio, Direct binomial sampling scheme, Inverse binomial sampling scheme, Asymptotic confidence limits, Logarithmic confidence interval, Monte Carlo simulation.