Identification and estimation of bounds on school performance measures: a nonparametric analysis of a mixture model with verification

This paper identifies and nonparametrically estimates sharp bounds on school performance measures based on test scores that may not be valid for all students. A mixture model with verification is developed to handle this problem. This is a mixture model for data that can be partitioned into two sets, one of which (the so-called verified set) is more likely to be from the distribution of interest than the other. An administrative classification of each student as English proficient or limited English proficient determines these sets. An analysis of performance measures for some California public schools reveals how verification information and plausible monotonicity restrictions can bound the range of disagreement about school performance based on observed scores.