Univariate Kernel Density Estimation

Provides an efficient implementation of univariate local polynomial kernel density estimators that can handle bounded, discrete, and zero-inflated data. See Geenens and Wang (2018) , Geenens (2014) , Nagler (2018a) , Nagler (2018b) .

kde1d

Summary

implements a univariate kernel density estimator that can handle bounded, discrete, and zero-inflated data.
provides classical kernel density as well as log-linear and log-quadratic methods.
is highly efficient due to the Fast Fourier Transform, spline interpolation, and a C++ backend.

For details, see the API documentation.

How to install

the stable release from CRAN:

install.packages("kde1d")

the latest development version:

# install.packages("remotes")
remotes::install_github("tnagler/kde1d@dev")

Examples

Unbounded data

x <- rnorm(100)                    # simulate data
fit <- kde1d(x)                    # estimate density
dkde1d(0, fit)                     # evaluate density estimate
summary(fit)                       # information about the estimate
plot(fit)                          # plot the density estimate
curve(dnorm(x), add = TRUE,        # add true density
      col = "red")

Bounded data, log-linear

x <- rgamma(100, shape = 1)        # simulate data
fit <- kde1d(x, xmin = 0, deg = 1) # estimate density
dkde1d(seq(0, 5, by = 1), fit)     # evaluate density estimate
summary(fit)                       # information about the estimate
plot(fit)                          # plot the density estimate
curve(dgamma(x, shape = 1),        # add true density
      add = TRUE, col = "red",
      from = 1e-3)

Discrete data

x <- rbinom(100, size = 5, prob = 0.5)  # simulate data
x <- ordered(x, levels = 0:5)           # declare as ordered
fit <- kde1d(x, xmin = 0, xmax = 5,     # estimate density
            type = "discrete") 
fit <- kde1d(ordered(x, levels = 0:5))  # alternative API
dkde1d(sort(unique(x)), fit)            # evaluate density estimate
summary(fit)                            # information about the estimate
plot(fit)                               # plot the density estimate
points(ordered(0:5, 0:5),               # add true density
       dbinom(0:5, 5, 0.5), col = "red")

Zero-inflated data data

x <- rexp(500, 0.5)                    # simulate data
x[sample(1:500, 200)] <- 0             # add zero-inflation
fit <- kde1d(x, xmin = 0, type = "zi") # estimate density
plot(fit)                              # plot the density estimate
lines(                                 # add true density        
  seq(0, 20, l = 100),
  0.6 * dexp(seq(0, 20, l = 100), 0.5),
  col = "red"
)
points(0, 0.4, col = "red")

Weighted estimate

x <- rnorm(100)                         # simulate data
weights <- rexp(100)                    # weights as in Bayesian bootstrap
fit <- kde1d(x, weights = weights)      # weighted fit
plot(fit)                               # compare with unweighted fit
lines(kde1d(x), col = 2)

References

Geenens, G. (2014). Probit transformation for kernel density estimation on the unit interval. Journal of the American Statistical Association, 109:505, 346-358, arXiv:1303.4121

Geenens, G., Wang, C. (2018). Local-likelihood transformation kernel density estimation for positive random variables. Journal of Computational and Graphical Statistics, 27(4), 822-835. arXiv:1602.04862

Loader, C. (2006). Local regression and likelihood. Springer Science & Business Media.

Nagler, T. (2018a). A generic approach to nonparametric function estimation with mixed data. Statistics & Probability Letters, 137:326–330, arXiv:1704.07457

Nagler, T. (2018b). Asymptotic analysis of the jittering kernel density estimator. Mathematical Methods of Statistics, 27, 32-46. arXiv:1705.05431