# Numerical Partial Derivative Estimation – the {NNS} package

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`NNS (v0.5.5)`

now on CRAN has an updated partial derivative routine ** dy.d_()** . This function estimates true average partial derivatives, as well as ceteris paribus conditions for points of interest.

Example below on the syntax for estimating first derivatives of the function `y = x_1^2 * x_2^2`

, for the points `x_1 = 0.5`

and ** x_2 = 0.5**, and for both regressors

**and**

`x_1`

`x_2`

.`set.seed(123)`

`x_1 = runif(1000)`

`x_2 = runif(1000)`

`y = x_1 ^ 2 * x_2 ^ 2`

```
```dy.d_(cbind(x_1, x_2), y, wrt = 1:2, eval.points = t(c(.5,.5)))["First",]

[[1]]

[1] 0.2454744

[[2]]

`[1] 0.2439307`

The analytical solution for both regressors at ** x_1 = x_2 = 0.5** is 0.25.

The referenced paper gives many more examples, comparing ** dy.d_()** to kernel regression gradients and OLS coefficients.

For even more `NNS`

capabilities, check out the examples at GitHub:

https://github.com/OVVO-Financial/NNS/blob/NNS-Beta-Version/examples/index.md

**Reference Paper:**

Vinod, Hrishikesh D. and Viole, Fred, *Comparing Old and New Partial Derivative Estimates from Nonlinear Nonparametric Regressions *

https://ssrn.com/abstract=3681104

**Supplemental Materials:**

https://ssrn.com/abstract=3681436

Numerical Partial Derivative Estimation – the {NNS} package was first posted on September 3, 2020 at 5:20 pm.

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