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One criticism of weight functions with bounded support is that they can lead to numerical problems (i.e. an unstable or singular design matrix) when fitting in regions with sparse data. For this reason, some authors choose to use the Gaussian kernel, or others with unbounded support.
===Choice of
As described above, local regression uses a locally weighted least squares criterion to estimate the regression parameters. This inherits many of the advantages (ease of implementation and interpretation; good properties when errors are normally distributed) and disadvantages (sensitivity to extreme values and outliers; inefficiency when errors have unequal variance or are not normally distributed) usually associated with least squares regression.
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