Choice of Global and Local Bandwidths
For practice applications of curve smoothing methods, the choice of a good smoothing parameter is a very important issue. For kernel and weighted local least squares estimators this is the choice of the bandwidth, which besides the choice of the correct order of the kernel or polynomial has a strong influence on the quality of the estimate. The smoothing parameter, losely speaking, provides information about the signal-to-noise ratio in the data; strongly oscillating measurements can be due to a strongly oscillating curve with small measurement errors or to a very smooth curve with large measurement errors. In many finite sample situations it is very difficult to make the right decision and to use correctly a small bandwidth in the first and a large bandwidth in the second case. Therefore a completely satisfying finite sample solution of the bandwidth choice problem is not possible. The methods proposed for bandwidth choice are motivated by asymptotic considerations. A comprehensive survey of the finite sample behavior in simulations of various methods of bandwidth choice seems not to exist so far.
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