# chooseLowessSpan: Choose Span for Local-Weighted Regression Smoothing In limma: Linear Models for Microarray Data

## Description

Choose an optimal span, depending on the number of points, for lowess smoothing of variance trends.

## Usage

 `1` ```chooseLowessSpan(n=1000, small.n=25, min.span=0.2, power=1/3) ```

## Arguments

 `n` the number of points the lowess curve will be applied to. `small.n` the span will be set to 1 for any `n` less than or equal to size value. `min.span` the minimum span for large `n`. `power` numeric power between 0 and 1 how fast the chosen span decreases with `n>`.

## Details

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`.

## Value

A numeric vector of length 1 containing the span value.

Gordon Smyth

## References

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.

`loessFit`, `weightedLowess`, `lowess`, `loess`.
`vooma`, `eBayes`, `squeezeVar`, `fitFDistRobustly`.
 ```1 2 3 4 5 6``` ```chooseLowessSpan(100) chooseLowessSpan(1e6) n <- 10:5000 span <- chooseLowessSpan(n) plot(n,span,type="l") ```