Integrated-Likelihood-Ratio Confidence Intervals Obtained from Data Via a Double-Sampling Scenario
Abstract
Hypothesis testing has been a primary focus of statistical inference. Recently, confidence intervals (CIs) have been suggested as a superior inference form because of the additional information they provide to a scientist to aid decision making. For public health data, business data, and other types of data, misclassification is often present and can cause estimators to be biased, thus leading to incorrect conclusions. Tenenbein (1970) has provided a double-sampling scheme to correct for misclassification through the use of an infallible data set that is combined with a larger fallible data set subject to misclassification. Many authors have utilized the double-sampling procedure to correct for misclassification in their data. When constructing confidence intervals, for instance, Rahardja and Yang (2015) derived Wald intervals for one-sample binomial problems, and Lyles (2002) proposed a Wald interval for two-sample binomial problems. Also, Riggs et al. (2009) provided confidence intervals for one-sample Poisson rate parameters. In addition, Li (2009) built similar intervals for the difference of two Poisson rate parameters. We derive integrated-likelihood-ratio (ILR) confidence intervals, first proposed by Severini (2010), for each of these situations to demonstrate their effectiveness in estimating parameters from data subject to misclassification. In chapter one, we derive an ILR CI for a one-sample binomial data set and demonstrate that it has at least nominal coverage while providing narrow average interval widths when the binomial parameter is small. In chapter two, we apply a transformation related to one from Fisher and Robbins (2019) to make the ILR CI less conservative when estimating a one-sample binomial parameter, thus providing closer-to-nominal coverage while decreasing the average interval width. In chapter three, we extend the ILR CI to estimate the log odds-ratio of two binomial parameters when the binary data are subject to misclassification. Finally, in chapter four we demonstrate the ILR CI’s efficacy versus the Wald and score CIs for estimating the ratio of two Poisson rate parameters using data sampled via a double-sampling scenario.
