Wilson Score Kernel Density Estimation for Bernoulli Trials

We propose a new function estimator, called Wilson Score Kernel Density Estimation, that allows to esti-mate a mean probability and the surrounding confidence interval for parameterized processes with binomiallydistributed outcomes. Our estimator combines the advantages of kernel smoothing, from Kernel Density Esti-mation, and robustness to low number of samples, from Wilson Score. This allows for more robust and dataefficient estimates compared to the individual use of these two estimators. While our estimator is generallyapplicable for processes with binomially distributed outcomes, we will present it in the context of iterativeoptimization. Here we first show the advantage of our estimator on a mathematically well defined problem,and then apply our estimator to an industrial automation process.