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kdensity is now in maintenance mode: future releases fix bugs and keep the package working on CRAN, but add no new features.
kernel = "gamma" now implements Chen’s (2000)
modified gamma kernel, a gamma density with scale h and
shape y / h for y >= 2h and
(y / (2h))^2 + 1 below. Earlier versions used a shape one
larger, so for y >= 2h the kernel coincided with the
uncorrected gamma_biased kernel and its boundary
modification increased the error. Every fit that uses the gamma kernel
changes, including the bandwidths selected for it.
Every built-in kernel now defaults to a closed-form bandwidth
rule, so no default needs cross-validation. A gamma-kernel fit at n =
10,000 took 48–198 seconds with the old "ucv" default; it
now takes milliseconds. The new defaults:
gamma and gamma_biased: "GR"
(was "ucv").beta and beta_biased: "HS"
(was "ucv", except for beta with a uniform
start).gcopula: "SJ" (was "JH" with
a uniform start and "ucv" otherwise). "JH"
oversmooths multimodal data badly, up to 29 times the optimal integrated
squared error in simulations.The rules ignore the parametric start, as "RHE" already
did for symmetric kernels, so they undersmooth a little when the start
fits well; bw = "ucv" remains available for a start-aware
choice. In simulations over gamma, exponential, lognormal, Weibull, beta
and mixture targets, the new defaults did as well as or better than
"ucv" with uniform starts.
bw = "SJ" with the gcopula kernel now
applies Sheather and Jones’s selector on the probit scale, where the
Gaussian copula estimator is a Gaussian kernel estimate, and converts
the result to the copula bandwidth. It previously applied the selector
to the raw data, which does not give a bandwidth for this
kernel.
Fitted kdensity objects are read-only. The
update(), $<- and [[<-
methods are removed, so kde$bw <- 0.5 now gives an
error. update() falls back to
stats::update.default(), which refits from the stored call
with the changed arguments (as for lm()) and returns a new
object: write kde <- update(kde, bw = 0.5). This also
makes update() work for fits with a numeric or
custom-function bandwidth. The data must be visible from where
update() is called.
Custom kernels and parametric starts must use names that differ
from the built-ins (for example my_gaussian). Before, a
custom kernel or start with a built-in name silently replaced it for the
rest of the session and disabled its compiled path. Re-registering a
custom name is still allowed.
kdensity_grid() evaluates a fit on a grid by linear
binning and FFT convolution, for every built-in symmetric kernel and for
the Gaussian-copula kernel (on the probit scale). It convolves with the
fitted kernel itself, so it also covers kernels that
stats::density() lacks (triweight, tricube, laplace). The
result is approximate; calling a kdensity object stays
exact.
plot(), lines() and
points() gain a grid argument. The default,
"auto", uses FFT for the Gaussian and Gaussian-copula
kernels and exact evaluation for the others, where it is as fast. Use
grid = "exact" or grid = "fft" to
choose.
New bandwidth selector "GR": Chen’s AMISE-optimal
bandwidth for the bias-corrected gamma kernel, with a fitted gamma
density in place of the unknown one. The fitted shape is floored at 3
(keeping the fitted mean), since the rule needs a shape above 3/2, and
exact zeros are left out of the reference fit.
bw = "ucv" for asymmetric kernels and for parametric
starts compared the integral of the squared normalized estimate
with unnormalized leave-one-out estimates. Both terms are now
normalized. Since the gamma kernels’ normalizing constant grows with the
bandwidth, the old criterion pulled strongly towards oversmoothing.
Symmetric kernels with a uniform start use stats::bw.ucv()
and are unaffected.
bw = "ucv" for the asymmetric kernels with a
non-uniform parametric start took the kernel’s shape from the wrong data
point, so the criterion did not match the estimator.
bw = "ucv" for the gamma, beta and Gaussian-copula
kernels now searches around a closed-form pilot on the kernel’s own
bandwidth scale, avoiding intervals that force oversmoothing. It warns
when the selected bandwidth is within 1% of either end of the search
interval.
logLik(), AIC() and BIC()
for fits with a parametric start summed the start’s densities instead of
their logarithms and reported nobs = 1. They now return the
start’s log-likelihood and the correct AIC and BIC.
The Gaussian-copula kernel constant is fixed, so unnormalized estimates with a uniform start integrate to one; normalized estimates are unchanged. Data at 0 or 1 now give an error suggesting the beta kernel or moving the observations off the boundary.
Gaussian-copula estimates at exactly 0 or 1 return their limit
instead of NaN, so plots and grids that start at the
boundary keep their end points.
Fits give a clear error when the fitted start has zero, negative
or non-finite density at an observation, instead of silently returning
NaN. Numeric bw = Inf still returns the
parametric start without this check.
The vectorized bias-corrected beta kernel no longer reorders the values from its lower, interior and upper sections.
Built-in kernels are evaluated exactly in compiled code, so installing from source now needs a C++17 compiler. Gaussian and Gaussian-copula evaluation is much faster, and the beta and gamma kernels reuse cached data transformations. User-supplied kernels keep the R path.
Compact-support kernels switch to exact sorted range sums once enough points have been evaluated, and the Laplace kernel uses an exact two-sweep recurrence, which speeds up large and repeated evaluations.
Exact normalizing constants replace numerical integration for ordinary symmetric KDEs, Gaussian-copula KDEs, and Gaussian kernels with a normal start. This also avoids spurious normalization failures for compact symmetric kernels.
bw = "ucv" gains compiled paths: the compiled
evaluator for built-in kernels with a uniform start, and a log-stable
pairwise path with batched leave-one-out estimates for normal,
exponential, lognormal, gamma, Weibull and beta starts. Gamma and beta
kernels reuse shape and normalization constants across observations.
Invalid compiled fits fall back to the R path.
"HS", based on
Hallberg Szabadváry’s beta reference rule (arXiv:2601.19553). It is now
the default bandwidth for the bias-corrected beta kernel
with a uniform or constant start, with a fallback heuristic when the
rule’s moment conditions are not satisfied.RHE no longer depends on the EQL package;
the Hermite polynomials are evaluated inline (matches the previous
numeric output to ~1e-12).EQL removed from
Imports; assertthat, testthat,
extraDistr, and other build-time helpers no longer required
at install time.R/ source layout is consolidated
into bandwidths.R, kernels.R,
starts.R, and helpers.R; no user-visible API
changes.laplace kernel.kdensity: Added error message when the normalization
constant fails to be accurate enough and a tolerance parameter to
control it.These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.