Gaussian Kernel Smoothing

Functions > Data Analysis > Smoothing > Gaussian Kernel Smoothing

Gaussian Kernel Smoothing

• ksmooth(vx, vy, b)—Returns a vector of local weighted averages of the elements in vy using a Gaussian kernel of bandwidth b, that is, smoothed elements of vy are given by:

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where

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The ksmooth function is most useful when your data lies along a band of relatively constant width. Bandwidth is usually set to a few times the spacing between data points on the x-axis, depending on the desired degree of smoothing.

Some types of data are better smoothed with one type of algorithm over another. You may wish to compare this method with median smoothing or localized least-squares smoothing. The loess polynomial regression technique is also an effective smoother.

Arguments

• vx is a vector of real numbers with elements in ascending order.

• vy is a vector of real numbers the same length as vx.

• b is the bandwidth of the smoothing window.