LowessFittings

Full name Microsoft.VisualBasic.Data.Bootstrapping.LowessFittings Assembly Microsoft.VisualBasic.Data.Bootstrapping.Fittings Members 3

01 Syntax

Microsoft.VisualBasic.Data.Bootstrapping.LowessFittings

02 Methods

Name	Overloads	Summary
Lowess	2	Locally-weighted polynomial regression via the LOWESS algorithm.
lowest	1	Calculates the fitted value ys for a value xs on the horizontal axis.

03 Members

method Lowess #

Lowess(IEnumerable(Of PointF), Double, Int32)

Locally-weighted polynomial regression via the LOWESS algorithm.

Parameters

Name	Type	Description
`sample`	`IEnumerable(Of PointF)`	-
`f`	`Double`	smoother span (proportion of points which influence smoothing at each value)
`nsteps`	`Int32`	number of iterations in the robust fit

method Lowess overload 2 #

Lowess(Double(), Double(), Int32, Double, Int32, Double)

Locally-weighted polynomial regression via the LOWESS algorithm.

Remarks

Calculates fitted values using a nearest neighbor function and robust locally weighted regression of degree one with the tricube weight function.

Cleveland, William S. 1979. "Robust Locally and Smoothing Weighted Regression Scatterplots." Journal of the American Statistical Association 74 (368): 829–36. doi:10.1080/01621459.1979.10481038.
Cleveland, William S. 1981. "Lowess: A program for smoothing scatterplots by robust locally weighted regression." American Statistician 35 (1) 54–55. doi:10.2307/2683591.

Parameters

Name	Type	Description
`x`	`Double()`	ordered x-axis values (abscissa values)
`y`	`Double()`	corresponding y-axis values (ordinate values)
`n`	`Int32`	number of observations
`f`	`Double`	smoother span (proportion of points which influence smoothing at each value)
`nsteps`	`Int32`	number of iterations in the robust fit
`delta`	`Double`	nonnegative parameter which may be used to reduce the number of computations

Returns

sorted x-values and fitted values

method lowest #

lowest(Double(), Double(), Int32, Int32, Int32, Int32, Double(), Boolean, Double())

Calculates the fitted value ys for a value xs on the horizontal axis.

Remarks

The smoothed value for the x-axis value at the current index is computed using a (robust) locally weighted regression of degree one. The tricube weight function is used with h equal to the maximum of xs - x[ nleft ] and x[ nright ] - xs.

Cleveland, William S. 1979. "Robust Locally and Smoothing Weighted Regression Scatterplots." Journal of the American Statistical Association 74 (368): 829–36. doi:10.1080/01621459.1979.10481038.
Cleveland, William S. 1981. "Lowess: A program for smoothing scatterplots by robust locally weighted regression." American Statistician 35 (1) 54–55. doi:10.2307/2683591.

Parameters

Name	Type	Description
`x`	`Double()`	ordered x-axis values (abscissa values)
`y`	`Double()`	corresponding y-axis values (ordinate values)
`n`	`Int32`	number of observations
`i`	`Int32`	current index
`nleft`	`Int32`	index of the first point used in computing the fitted value
`nright`	`Int32`	index of the last point used in computing the fitted value
`w`	`Double()`	weights at indices from `nleft` to `nright` to be used in the calculation of the fitted value
`userw`	`Boolean`	boolean indicating whether a robust fit is carried out using the weights in `rw`
`rw`	`Double()`	robustness weights

Returns

fitted value