Wilson Score Kernel Density Estimation For Bernoulli Trials

We propose a new function estimator, called Wilson Score Kernel Density Estimation, that allows to estimate a mean probability and the surrounding confidence interval for parameterized processes with binomially distributed outcomes. Our estimator combines the advantages of kernel smoothing, from Kernel Density Estimation, and robustness to low number of samples, from Wilson Score. This allows for more robust and data efficient estimates compared to the individual use of these two estimators. While our estimator is generally applicable for processes with binomially distributed outcomes, we will present it in the context of iterative optimization. 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.