Choose Span for Local-Weighted Regression Smoothing
Choose an optimal span, depending on the number of points, for lowess smoothing of variance trends.
chooseLowessSpan(n=1000, small.n=25, min.span=0.2, power=1/3)
n |
the number of points the lowess curve will be applied to. |
small.n |
the span will be set to 1 for any |
min.span |
the minimum span for large |
power |
numeric power between 0 and 1 how fast the chosen span decreases with |
The span is the proportion of points used for each of the local regressions. When there a few points, a large span should be used to ensure a smooth curve. When there are a large number of points, smaller spans can be used because each span window still contains good coverage. By default, the chosen span decreases as the cube-root of the number of points, a rule that is motivated by analogous rules to choose the number of bins for a histogram (Scott, 1979; Freedman & Diaconis, 1981; Hyndman, 1995).
The span returned is essentially
min.span + (1-min.span) * (small.n/n)^power.
The span is set to 1 for any n less than small.n.
The function is tuned for smoothing of mean-variance trends, for which the trend is usually monotonic, so preference is given to moderately large spans.
Even for the large datasets, the span is always greater than min.span.
This function is used to create the default span for vooma, eBayes, squeezeVar and fitFDistRobustly.
A numeric vector of length 1 containing the span value.
Gordon Smyth
Freedman, D. and Diaconis, P. (1981). On the histogram as a density estimator: L_2 theory. Zeitschrift fur Wahrscheinlichkeitstheorie und verwandte Gebiete, 57, 453-476.
Hyndman, R. J. (1995). The problem with Sturges' rule for constructing histograms. http://robjhyndman.com/papers/sturges.pdf.
Scott, D. W. (1979). On optimal and data-based histograms. Biometrika, 66, 605-610.
chooseLowessSpan(100) chooseLowessSpan(1e6) n <- 10:5000 span <- chooseLowessSpan(n) plot(n,span,type="l")
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