Paradoxes and improvements in interval estimation

Cases where confidence sets are empty or include every possible parameter v alue are an embarrassment to standard theory and difficult to explain to st udents. To alleviate this problem, and as a convenient way of showing how e ach parameter value is ranked in view of the data, we propose to plot the c onfidence set for each possible level, called a confidence curve. Different confidence procedures then lead to different confidence curves. In standar d situations involving distributions with a monotone likelihood ratio, we s uggest using the confidence curve based on Spjotvoll's acceptability functi on. For discrete distributions, this leads to an improvement over usual "ex act" confidence intervals.