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One question not addressed above is, how should the bandwidth depend upon the fitting point <math>x</math>? Often a constant bandwidth is used, while LOWESS and LOESS prefer a nearest-neighbor bandwidth, meaning ''h'' is smaller in regions with many data points. Formally, the smoothing parameter, <math>\alpha</math>, is the fraction of the total number ''n'' of data points that are used in each local fit. The subset of data used in each weighted least squares fit thus comprises the <math>n\alpha</math> points (rounded to the next largest integer) whose explanatory variables' values are closest to the point at which the response is being estimated.<ref name="NIST">NIST, [http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd144.htm "LOESS (aka LOWESS)"], section 4.1.4.4, ''NIST/SEMATECH e-Handbook of Statistical Methods,'' (accessed 14 April 2017)</ref>
More sophisticated methods attempt to choose the bandwidth ''adaptively''; that is, choose a bandwidth at each fitting point <math>x</math> by applying criteria such as cross-validation locally within the smoothing window. An early example of this is [[Jerome H. Friedman]]'s<ref>{{citation|first=Jerome H.|last=Friedman|title=A Variable Span Smoother|date=October 1984|publisher=Technical report, Laboratory for Computational Statistics LCS 5; SLAC PUB-3466|doi=10.2171/1447470|doi-broken-date=
===Degree of local polynomials===
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