Nonparametric Knn estimation with monotone constraints

The K-nearest-neighbor (Knn) method is known to be more suitable in fitting nonparametrically specified curves than the kernel method (with a globally fixed smoothing parameter) when data sets are highly unevenly distributed. In this paper, we propose to estimate a nonparametric regression function subject to a monotonicity restriction using the Knn method. We also propose using a new convergence criterion to measure the closeness between an unconstrained and the (monotone) constrained Knn-estimated curves. This method is an alternative to the monotone kernel methods proposed by Hall and Huang (2001), and Du et al. (2013). We use a bootstrap procedure for testing the validity of the monotone restriction. We apply our method to the “Job Market Matching” data taken from Gan and Li (2016) and find that the unconstrained/constrained Knn estimators work better than kernel estimators for this type of highly unevenly distributed data.