dy.d_ {NNS}

Partial Derivative dy/d_[wrt]

Description

Returns the numerical partial derivative 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.

Usage

dy.d_(x, y, wrt, eval.points = "obs", mixed = FALSE, messages = TRUE)

Arguments

x

a numeric matrix or data frame.

y

a numeric vector with compatible dimensions to x.

wrt

integer; Selects the regressor to differentiate with respect to (vectorized).

eval.points

numeric or options: ("obs", "apd", "mean", "median", "last"); Regressor points to be evaluated.

• Numeric values must be in matrix or data.frame form to be evaluated for each regressor, otherwise, a vector of points will evaluate only at the wrt regressor. See examples for use cases.

• Set to (eval.points = "obs") (default) to find the average partial derivative at every observation of the variable with respect to for specific tuples of given observations.

• Set to (eval.points = "apd") to find the average partial derivative at every observation of the variable with respect to over the entire distribution of other regressors.

• Set to (eval.points = "mean") to find the partial derivative at the mean of value of every variable.

• Set to (eval.points = "median") to find the partial derivative at the median value of every variable.

• Set to (eval.points = "last") to find the partial derivative at the last observation of every value (relevant for time-series data).

mixed

logical; FALSE (default) If mixed derivative is to be evaluated, set (mixed = TRUE).

messages

logical; TRUE (default) Prints status messages.

Value

Returns column-wise matrix of wrt regressors:

• dy.d_(...)[, wrt]$First the 1st derivative

• dy.d_(...)[, wrt]$Second the 2nd derivative

• dy.d_(...)[, wrt]$Mixed the mixed derivative (for two independent variables only).

Note

For binary regressors, it is suggested to use eval.points = seq(0, 1, .05) for a better resolution around the midpoint.

Author(s)

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp

Vinod, H. and Viole, F. (2020) "Comparing Old and New Partial Derivative Estimates from Nonlinear Nonparametric Regressions" https://www.ssrn.com/abstract=3681104

Examples

## Not run: 
set.seed(123) ; x_1 <- runif(1000) ; x_2 <- runif(1000) ; y <- x_1 ^ 2 * x_2 ^ 2
B <- cbind(x_1, x_2)

## To find derivatives of y wrt 1st regressor for specific points of both regressors
dy.d_(B, y, wrt = 1, eval.points = t(c(.5, 1)))

## To find average partial derivative of y wrt 1st regressor,
only supply 1 value in [eval.points], or a vector of [eval.points]:
dy.d_(B, y, wrt = 1, eval.points = .5)

dy.d_(B, y, wrt = 1, eval.points = fivenum(B[,1]))


## To find average partial derivative of y wrt 1st regressor,
for every observation of 1st regressor:
apd <- dy.d_(B, y, wrt = 1, eval.points = "apd")
plot(B[,1], apd[,1]$First)

## 95% Confidence Interval to test if 0 is within
### Lower CI
LPM.VaR(.025, 0, apd[,1]$First)

### Upper CI
UPM.VaR(.025, 0, apd[,1]$First)

## End(Not run)