Density, Distribution, Quantiles

Practical route to unconditional and conditional density/distribution workflows, plus nonparametric quantile regression in np.
Keywords

npudens, npudist, npcdens, npcdist, npqreg, density, quantile regression

The np package is useful not only for regression but also for unconditional and conditional density estimation, distribution estimation, and nonparametric quantile regression. This page collects those workflows in one place.

If you want a minimal downloadable script for the simplest density workflow, start with np_density_quickstart.R.

If you want the shortest route to conditional density or quantile workflows, start with:

Unconditional density and distribution: npudens and npudist

Use these when the object of interest is the joint or marginal distribution itself rather than a regression function.

The Old Faithful data remain a simple and informative illustration because the shape is not well summarized by a simple parametric family.

library(np)
data(faithful, package = "datasets")

f_faithful <- npudens(~ eruptions + waiting, data = faithful)
F_faithful <- npudist(~ eruptions + waiting, data = faithful)

summary(f_faithful)
summary(F_faithful)

If you want to visualize the estimated surface, you can then plot the objects.

plot(f_faithful, view = "fixed", main = "")
plot(F_faithful, view = "fixed", main = "")

This is a good example of why nonparametric methods can matter: a bimodal or otherwise irregular structure is much easier to reveal when you do not force a simple parametric family on the data.

Conditional density and distribution: npcdens and npcdist

Use these when the full conditional distribution matters, not just the conditional mean.

The old GDP panel example remains helpful because the conditional distribution changes shape over time.

library(np)
data(Italy, package = "np")

fhat <- npcdens(gdp ~ year, data = Italy)
Fhat <- npcdist(gdp ~ year, data = Italy)

summary(fhat)
summary(Fhat)

Plots can then be used to inspect the evolving conditional density and conditional distribution.

plot(fhat, view = "fixed", main = "")
plot(Fhat, view = "fixed", main = "")

This route is especially useful when the question is not simply whether the mean changes, but whether the entire distribution changes.

Nonparametric quantile regression: npqreg

Use npqreg when your interest lies in conditional quantiles rather than means.

One natural workflow is:

  1. compute a conditional-distribution bandwidth object,
  2. reuse it for multiple quantiles.
library(np)
data(Italy, package = "np")

bw <- npcdistbw(gdp ~ year, data = Italy)
q25 <- npqreg(bws = bw, tau = 0.25)
q50 <- npqreg(bws = bw, tau = 0.50)
q75 <- npqreg(bws = bw, tau = 0.75)

Then compare the fitted quantiles:

plot(Italy$year, Italy$gdp, main = "", xlab = "Year", ylab = "GDP Quantiles")
lines(Italy$year, q25$quantile, col = "red", lty = 1, lwd = 2)
lines(Italy$year, q50$quantile, col = "blue", lty = 2, lwd = 2)
lines(Italy$year, q75$quantile, col = "red", lty = 3, lwd = 2)

This is a good example of when it pays to separate bandwidth selection from later estimation rather than recomputing the same object repeatedly.

When should I use these instead of regression?

If you want… Start with
A regression function or conditional mean npreg
An unconditional density or distribution npudens, npudist
A conditional density or conditional distribution npcdens, npcdist
Conditional quantiles npqreg

Practical advice

  • density and conditional-density workflows can be computationally heavier than users expect,
  • use explicit bandwidth objects when reusing the same structure across multiple fits,
  • plots are often the most informative part of the workflow,
  • if the run becomes expensive and the workflow is stable, that may be a reason to move to npRmpi.
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