Conditional Confidence Intervals Research Articles

Simulation Study of Conditional, Bootstrap, and t Confidence Intervals in Linear Regression

Two resampling procedures, the bootstrap (BS) and the conditional confidence interval (CCI), are compared with the standard t-interval for the slope parameter in simple linear regression with an error term that is not necessarily normal. The type of bootstrap confidence intervals computed are the widely used bias-corrected and accelerated (BC a ) intervals. The CCIs are found by an efficient method for inverting permutation tests. Normal, highly skewed, and heavy-tailed error distributions are considered. While the CCI and BC a intervals have similar asymptotic properties, for a moderate number of cases, the confidence intervals obtained from the CCI and BC a behave differently in terms of accuracy, power, length, and correctness. Across all conditions, the CCI is the most accurate interval and has very good power. The t-intervals are also very accurate across most of the conditions we studied, and have coverage closer to the nominal value than the BC a intervals.

Conditional Interval Estimation of the Ratio of Variance Components following Rejection of a Pre-test

The conditional confidence interval for a ratio of variance components in the random effects model and the random effects nested design following a preliminary test is investigated. The conditional confidence interval (CCI) may be shorter than the unconditional confidence interval (UCI) in contrast to the findings for the mean of a normal distribution by Meeks and D'Agostino (1983). The conditional coverage probability of the UCI is obtained by computing the coverage probability under the conditional probability density function. It is shown that the conditional coverage pobability of the UCI is not uniformly greater than or less than the nominal level. The UCI is appropriate only when one does not perform any pre-test. However, if a pre-test is performed before the construction of a confidence interval, then the appropriate confidence interval is the CCI because the pre-test affects subsequent inference procedures.

Trimmed conditional confidence intervals for a shift between two populations

The trimmed conditional confidence interval (CCI) is introduced for estimating the shift between two populations. The trimmed CCI is compared to an untrimmed CCI and to intervals obtained from the trimmed mean the usual t-procedure and the bootstrap. The simulations show that the trimmed CCI generates the shortest intervals while maintaining coverage rates at the nominal level. The untrimmed CCI is reasonably robust with respect to moderate departures from the procedural assumptions and performs well compared to the nontrimmed procedures. Both versions of the CCI are calculated easily and are suitable for use in an interactive setting. SAS and S code for obtained the CCI are available from the authors.

Conditional interval estimation of the extreme-value scale parameter following rejection of a pre-test

A conditional confidence interval for the scale parameter of the extrernevalue distribution following a preliminary test is investigated. The conditional confidence interval (CCI) may be shorter than the unconditional confidence interval (UCI) in contrast to the findings for the mean of a normal distribution by Meeks and D'Agostino (1983). The conditional coverage probability of the UCI is obtained by computing the coverage probability under the conditional probability density function. It is shown that the conditional coverage probability of the UCI is not uniformly greater than or less than the nominal level. The UCI is appropriate only when one does not perform any pre-test. However, if a pre-test is performed before the constructicin of a confidence interval, then the appropriate confidence interval is the CCI because the pre-test affects subsequent inference procedures.

Conditional interval estimation of the exponential location parameter following rejection of a pre-test

The conditional confidence interval for the location parameter of an exponential distribution following a preliminary test is investigated. The conditional confidence interval (CCI) may be shorter than the unconditional confidence interval (UCI) in contrast to the findings for the mean of a normal distribution by Meeks and D'Agostino (1983). The conditional coverage probability of the UCI is obtained by computing the coverage probability under the conditional probability density function. It is shown that the conditional coverage probability of the UCI is not uniformly greater than or less than the nominal level.