Nonparametric Knn estimation with monotone constraints
针对数据分布高度不均匀的情况，提出用K近邻方法估计带单调性约束的非参数回归函数，并给出新的收敛准则和检验方法，在就业市场匹配数据上表现优于核方法。
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 Hall, P., Huang, L.-S. (2001). Nonparametric kernel regression subject to monotonicity constraints. The Annals of Statistics 29:624–647.[Crossref], [Web of Science ®] , [Google Scholar]), and Du et al. (2013 Du, P., Parmeter, C. F., Racine, J. S. (2013). Nonparametric kernel regression with multiple predictors and multiple shape constraints. Statistic Sinica 23:1347–1371.[Web of Science ®] , [Google Scholar]). 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 Gan, L., Li, Q. (2016). Efficiency of thin and thick market. Journal of Econometrics 192(1):40–54.[Crossref], [Web of Science ®] , [Google Scholar]) and find that the unconstrained/constrained Knn estimators work better than kernel estimators for this type of highly unevenly distributed data.