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Local Polynomials at a Boundary
Kernels, bandwidth and polynomial order: boundary bias of local constant fits and how local linear fixes it.
Day 74: Local Polynomial Regression & Kernelsestimate at the boundary
9.84
truth 10.00
observations used
79
bias (300 samples)
0.058
SD (300 samples)
0.210
Estimating a regression function at the edge of its support (x = 0, true value 10), as on one side of an RD cutoff. Point size shows each observation's kernel weight. A local constant fit (order 0) is pulled up by the slope; local linear removes that first-order bias; local quadratic removes curvature bias at the cost of variance. Bias and SD come from 300 simulated samples.