Robust likelihood inference for public policy

Issues of public policy are typically decided by non‐specialists who are increasingly informed by statistical methods. In order to be influential, inferential techniques must be widely understood and accepted. This motivates the author to propose likelihood‐based methods that prove relatively insensitive to the choice of underlying distribution because they exploit a peculiarly stable relation between two standard errors and a 95% coverage probability. The author also notes that bootstrap and jackknife estimates of variance can sometimes be strongly biased. In fact, symbolic computations in R suggest that they are reliable only for statistics that are well approximated by averages whose distributions are roughly symmetric. The author thus proposes to transform the classical likelihood ratio into a statistic whose variance can be estimated robustly. He shows that the signed root of the log‐likelihood is well approximated by an average with a roughly symmetric distribution. This leads to Cox‐Tukey intervals for a Student‐like statistic and to simple confidence intervals for most models used in public policy.