Description Usage Arguments Value Note Author(s) References Examples

Returns the numerical partial derivate of `y`

with respect to [wrt] any regressor for a point of interest. Finite difference method is used with NNS.reg estimates as `f(x + h)`

and `f(x - h)`

values.

1 2 3 |

`x` |
a numeric matrix or data frame. |

`y` |
a numeric vector with compatible dimsensions to |

`wrt` |
integer; Selects the regressor to differentiate with respect to. |

`eval.points` |
numeric or options: ("mean", median", "last"); Regressor points to be evaluated. |

`order` |
integer; NNS.reg |

`stn` |
numeric [0, 1]; Signal to noise parameter, sets the threshold of NNS.dep which reduces |

`h` |
numeric [0, ...]; Percentage step used for finite step method. Defaults to |

`n.best` |
integer; Sets the number of closest regression points to use in estimating finite difference points in NNS.reg. |

`mixed` |
logical; |

`plot` |
logical; |

`noise.reduction` |
the method of determing regression points options: ("mean", "median", "mode", "off"); In low signal to noise situations, |

Returns:

`dy.d_(...)$"First Derivative"`

the 1st derivative`dy.d_(...)$"Second Derivative"`

the 2nd derivative`dy.d_(...)$"Mixed Derivative"`

the mixed derivative (for two independent variables only).

Retuns a vector of partial derivatives when `(eval.points = "all")`

.

For known function testing and analysis, regressors should be transformed via expand.grid to fill the dimensions with `(order = "max")`

. Example provided below.

Fred Viole, OVVO Financial Systems

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

1 2 3 4 5 6 7 8 9 | ```
set.seed(123) ; x_1 <- runif(100) ; x_2 <- runif(100) ; y <- x_1 ^ 2 * x_2 ^ 2
B = cbind(x_1, x_2)
## To find derivatives of y wrt 1st regressor
dy.d_(B, y, wrt = 1, eval.points = c(.5, .5))
## Known function analysis: [y = a ^ 2 * b ^ 2]
x_1 <- seq(0, 1, .1) ; x_2 <- seq(0, 1, .1)
B = expand.grid(x_1, x_2) ; y <- B[ , 1] ^ 2 * B[ , 2] ^ 2
dy.d_(B, y, wrt = 1, eval.points = c(.5, .5), order = "max")
``` |

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