Location Characteristics of Conditional Selective Confidence Intervals via Polyhedral Methods

We examine the location characteristics of a conditional selective confidence interval based on the polyhedral method. This interval is constructed from the distribution of a test statistic conditional upon the event of statistical significance. In the case of a one-sided test, the behavior of the interval varies depending on whether the parameter is highly significant or only marginally significant. When the parameter is highly significant, the interval is similar to the usual confidence interval derived without considering selection. However, when the parameter is only marginally significant, the interval falls into an extreme range and deviates greatly from the estimated value of the parameter. In contrast, an interval conditional on two-sided significance does not yield extreme results, although it may exclude the estimated parameter value.