Faculty host Jon Wellner
Columbia University - Statistics
We consider estimation and inference in a two component mixture model where the distribution of one component is completely unknown. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d. data from the mixture model. We use ideas from shape restricted function estimation and develop "tuning parameter free" estimators that are easily implementable and have good finite sample performance. We establish the consistency of our procedures. Distribution-free finite sample lower confidence bounds are developed for the mixing proportion. We further generalize the two component mixture model to a regression context and develop estimation techniques. We discuss the connection with the problem of multiple testing and compare our procedure with some of the existing methods in this area through simulation studies.