Density estimation on a network

A novel approach is proposed for density estimation on a network. Nonparametric network formulated as nonparametric regression problem by binning. using local polynomial kernel-weighted least squares have been studied rigorously, and its asymptotic properties make it superior to kernel estimators such the Nadaraya–Watson estimator. When applied network, best estimator near vertex depends amount of smoothness at vertex. Often, there are no compelling reasons assume that will be continuous or discontinuous vertex, hence data driven proposed. To estimate in neighborhood two-step procedure The first step this pretest fits separate each edge only edge, then tests equality estimates If null hypothesis not rejected, second re-estimates function small subject joint constraint. Since derivative may piecewise used model change slope. special case linear detail leading bias variance terms derived weighted theory. remove has noted existing methods, which typically do allow discontinuity vertices. For fixed method scales sub-linearly with sample size can extended varying coefficient models working demonstrated simulation studies applications dendrite dataset.