# dy.dx: Partial Derivative dy/dx In NNS: Nonlinear Nonparametric Statistics

## Description

Returns the numerical partial derivate of `y` wrt `x` for a point of interest.

## Usage

 ```1 2 3``` ```dy.dx(x, y, order = NULL, stn = 0.99, eval.point = median(x), deriv.order = 1, h = 0.05, noise.reduction = "mean", deriv.method = "FS") ```

## Arguments

 `x` a numeric vector. `y` a numeric vector. `order` integer; Controls the number of partial moment quadrant means. Defaults to `(order=NULL)` which generates a more accurate derivative for well specified cases. `stn` numeric [0,1]; Signal to noise parameter, sets the threshold of NNS.dep which reduces `"order"` when `(order=NULL)`. Defaults to 0.99 to ensure high dependence for higher `"order"` and endpoint determination. `eval.point` numeric; `x` point to be evaluated. Defaults to `(eval.point=median(x))`. Set to `(eval.point="overall")` to find an overall partial derivative estimate. `deriv.order` numeric options: (1,2); 1 (default) for first derivative. For second derivative estimate of `f(x)`, set `(deriv.order=2)`. `h` numeric [0,...]; Percentage step used for finite step method. Defaults to `h=.05` representing a 5 percent step from the value of the independent variable. `noise.reduction` the method of determing regression points options: ("mean","median","mode","off"); In low signal to noise situations, `(noise.reduction="median")` uses medians instead of means for partitions, while `(noise.reduction="mode")` uses modes instead of means for partitions. `(noise.reduction="off")` allows for maximum possible fit in NNS.reg. Default setting is `(noise.reduction="mean")`. `deriv.method` method of derivative estimation, options: ("NNS","FS"); Determines the partial derivative from the coefficient of the NNS.reg output when `(deriv.method="NNS")` or generates a partial derivative using the finite step method `(deriv.method="FS")` (Defualt).

## Value

Returns the value of the partial derivative estimate for the given order.

## Note

If a vector of derivatives is required, ensure `(deriv.method="FS")`.

## Author(s)

Fred Viole, OVVO Financial Systems

## References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" http://amzn.com/1490523995

Vinod, H. and Viole, F. (2017) "Nonparametric Regression Using Clusters" https://link.springer.com/article/10.1007/s10614-017-9713-5

## Examples

 ```1 2 3 4 5``` ```x<-seq(0,2*pi,pi/100); y<-sin(x) dy.dx(x,y,eval.point=1.75) # Vector of derivatives dy.dx(x,y,eval.point=1.75,deriv.method="FS") ```

NNS documentation built on Feb. 17, 2018, 1:03 a.m.