JonesCorrectionMuller91BoundaryKernel {bde}

Class "JonesCorrectionMuller91BoundaryKernel"

Description

This class deals with nonnegative boundary correction of the muller91BoundaryKernel estimators for bounded densities. In this normalization, two kernel functions are needed. The first kernel funciton -K(u)- is the kernel function used in muller91BoundaryKernel (using left boundary, interior or right boundary kernel functions as needed). For the second kernel function, the popular choice L(u) = u * K(u) is taken. The kernel estimator is computed using the provided data samples. Using this kernel estimator, the methods implemented in the class can be used to compute densities, values of the distribution function, quantiles, sample the distribution and obtain graphical representations. Note that the renormalization of this kernel estimator guarantees nonnegative values for the density function but the cumulative density function may takes values greater than 1.

Objects from the Class

Objects can be created by using the generator function jonesCorrectionMuller91BoundaryKernel.

Slots

dataPointsCache:

a numeric vector containing points within the [lower.limit,upper.limit] interval

densityCache:

a numeric vector containing the density for each point in dataPointsCache

distributionCache:

a numeric vector used to cache the values of the distribution function. This slot is included to improve the performance of the methods when multiple calculations of the distribution function are used

dataPoints:

a numeric vector containing data samples within the [lower.limit,upper.limit] interval. These data samples are used to obtain the kernel estimator

b:

the bandwidth of the kernel estimator

mu:

a integer value indicating the degree of smoothness for the boundary kernel. mu can take the following values: 0 (uniform kernel), 1 (Epanechnikov kernel), 2 (biweight kernel) or 3 (triweight kernel)

normalizedKernel:

this slot is used to save a NormalizedBoundaryKernel object used in the normalization. It is only for internal use

lower.limit:

a numeric value for the lower limit of the bounded interval for the data

upper.limit:

a numeric value for the upper limit of the bounded interval for the data

Methods

density

See "density" for details

distribution

See "distribution" for details

quantile

See "quantile" for details

rsample

See "rsample" for details

plot

See "plot" for details

getdataPointsCache

See "getdataPointsCache" for details

getdensityCache

See "getdensityCache" for details

getdistributionCache

See "getdistributionCache" for details

getdataPoints

See "getdataPoints" for details

getb

See "getb" for details

getmu

See "getmu" for details

Author(s)

Guzman Santafe, Borja Calvo and Aritz Perez

References

Jones, M. C. and Foster, P. J. (1996). A simple nonnegative boundary correction method for kernel density estimation. Statistica Sinica, 6, 1005-1013.

Muller, H. (1991). Smooth optimum kernel estimators near endpoints. Biometrika, 78(3), 521-530.

Examples

# create the model 
kernel <-jonesCorrectionMuller91BoundaryKernel(dataPoints = tuna.r, b = 0.01, mu = 2)


# examples of usual functions
density(kernel,0.5)

distribution(kernel,0.5,discreteApproximation=FALSE)
 
# graphical representation
hist(tuna.r,freq=FALSE,main="Tuna Data")
lines(kernel, col="red",lwd=2)

# graphical representation using ggplot2 
graph <- gplot(kernel, show=TRUE, includePoints=TRUE)