density.reflected: Kernel Density Estimation with Reflection

In GoFKernel: Testing Goodness-of-Fit with the Kernel Density Estimator

Kernel Density Estimation with Reflection

Description

The function density.reflected computes kernel density estimates for univariate observations using reflection in the borders.

Usage

## S3 method for class 'reflected'
density(x, lower = -Inf, upper = Inf, weights= NULL, ...)

Arguments

x	a numeric vector of data from which the estimate is to be computed.
lower	the lower limit of the interval to which x is theoretically constrained, default -Inf.
upper	the upper limit of the interval to which x is theoretically constrained, default, Inf.
weights	numeric vector of non-negative observation weights, hence of same length as x. The default NULL is equivalent to weights = rep(1/length(x), length(x)).
...	further density arguments.

Details

density.reflected is called by dgeometric.test and computes the density kernel estimate of a univariate random sample x of a random variable defined in the interval (lower,upper) using the default options of density and reflection in the borders. This avoids the density kernel estimate being underestimated in the proximity of lower or upper. For unbounded variables, density.reflected generates the same output as density with its default options.

Value

An object of the class density with borders correction, whose underlying structure is a list containing the following components.

x	the n coordinates of the points where the density is estimated.
y	the estimated density values. These will be non-negative.
bw	the bandwidth used.
n	the sample size after elimination of missing values.
call	the call which produced the result.
data.name	the deparsed name of the x argument.
has.na	logical, for compatibility (always FALSE).

The print method reports summary values on the x and y components.

Note

The function is based on density.

Author(s)

Jose M. Pavia

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) "The New S Language." Wadsworth & Brooks/Cole (for S version).

Scott, D. W. (1992) "Multivariate Density Estimation. Theory, Practice and Visualization." New York: Wiley.

Sheather, S. J. and Jones M. C. (1991) "A reliable data-based bandwidth selection method for kernel density estimation." J. Roy. Statist. Soc. B, 683–690.

Silverman, B. W. (1986) "Density Estimation." London: Chapman and Hall.

Venables, W. N. and Ripley, B. D. (2002) "Modern Applied Statistics with S." New York: Springer.

See Also

dgeometric.test and density

Examples

set.seed(234)
x <- runif(2000)
dx <- density.reflected(x,0,1)

## Plot of the density estimate with and without reflection
par(mfcol=c(1,2))
plot(dx, xlim=c(-0.1,1.1), ylim=c(0,1.1))
abline(h=1, col="red")

plot(density(x), xlim=c(-0.1,1.1), ylim=c(0,1.1))
abline(h=1, col="blue")

GoFKernel documentation built on April 4, 2025, 2:47 a.m.