kade {kader}

Kernel Adaptive Density Estimator

Description

Wrapper function which does some preparatory calculations and then calls the actual “workhorse” functions which do the main computations for kernel adaptive density estimation of Srihera & Stute (2011) or Eichner & Stute (2013). Finally, it structures and returns the obtained results. Summarizing information and technical details can be found in Eichner (2017).

Usage

kade(x, data, kernel = c("gaussian", "epanechnikov", "rectangular"),
  method = c("both", "ranktrafo", "nonrobust"), Sigma = seq(0.01, 10, length
  = 51), h = NULL, theta = NULL, ranktrafo = J2, ticker = FALSE,
  plot = FALSE, parlist = NULL, ...)

Arguments

x

Vector of location(s) at which the density estimate is to be computed.

data

Vector (X_1, \ldots, X_n) of the data from which the estimate is to be computed. NAs or infinite values are removed (and a warning is issued).

kernel

A character string naming the kernel to be used for the adaptive estimator. This must partially match one of "gaussian", "rectangular" or "epanechnikov", with default "gaussian", and may be abbreviated to a unique prefix. (Currently, this kernel is also used for the initial, non-adaptive Parzen-Rosenblatt estimator which enters into the estimators of bias and variance as described in the references.)

method

A character string naming the method to be used for the adaptive estimator. This must partially match one of "both", "ranktrafo" or "nonrobust", with default "both", and may be abbreviated to a unique prefix.

Sigma

Vector of value(s) of the scale parameter \sigma. If of length 1 no adaptation is performed. Otherwise considered as the initial grid over which the optimization of the adaptive method will be performed. Defaults to seq(0.01, 10, length = 51).

h

Numeric scalar for bandwidth h. Defaults to NULL and is then internally set to n^{-1/5}.

theta

Numeric scalar for value of location parameter \theta. Defaults to NULL and is then internally set to the arithmetic mean of x_1, \ldots, x_n.

ranktrafo

Function used for the rank transformation. Defaults to J2 (with its default cc = sqrt(5)).

ticker

Logical; determines if a 'ticker' documents the iteration progress through Sigma. Defaults to FALSE.

plot

Logical or character or numeric and indicates if graphical output should be produced. Defaults to FALSE (i.e., no graphical output is produced) and is passed to adaptive_fnhat() which does the actual work. For details on how it is processed see there.

parlist

A list of graphical parameters that is passed to adaptive_fnhat(); see there. Default: NULL.

...

Further arguments possibly passed down. Currently ignored.

Value

In the case of only one method a data frame whose components have the following names and meanings:

x	x_0.
y	Estimate of f(x_0).
sigma.adap	The found minimizer of the MSE-estimator, i.e., the adaptive smoothing parameter value.
msehat.min	The found minimum of the MSE-estimator.
discr.min.smaller	TRUE iff the numerically found minimum was smaller than the discrete one.
sig.range.adj	Number of adjustments of sigma-range.

In the case of both methods a list of two data frames of the just described structure.

References

Srihera & Stute (2011), Eichner & Stute (2013), and Eichner (2017): see kader.

Examples

require(stats)

 # Generating N(0,1)-data
set.seed(2017);     n <- 80;     d <- rnorm(n)

 # Estimating f(x0) for one sigma-value
x0 <- 1
(fit <- kade(x = x0, data = d, method = "nonrobust", Sigma = 1))

 # Estimating f(x0) for sigma-grid
x0 <- 1
(fit <- kade(x = x0, data = d, method = "nonrobust",
  Sigma = seq(0.01, 10, length = 10), ticker = TRUE))

## Not run: 
 # Estimating f(x0) for sigma-grid and Old-Faithful-eruptions-data
x0 <- 2
(fit <- kade(x = x0, data = faithful$eruptions, method = "nonrobust",
  Sigma = seq(0.01, 10, length = 51), ticker = TRUE, plot = TRUE))

## End(Not run)