# 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 6 7 8 9``` ```## Not run: x <- seq(0, 2 * pi, pi / 100) ; y <-sin(x) dy.dx(x, y, eval.point = 1.75) ## End(Not run) # Vector of derivatives ## Not run: dy.dx(x, y, eval.point = c(1.75, 2.5), deriv.method = "FS") ## End(Not run) ```

NNS documentation built on May 15, 2019, 1:05 a.m.