hcvreg.fun {Ake}

Cross-validation function for bandwidth selection in regresssion

Description

The (S3) generic function hcvreg.fun computes the bandwidth by cross-validation for the regression. Its default method does so. It allows to compute the optimal bandwidth using the cross-validation method. The associated kernels available are: "BE" extended beta, "GA" gamma, "LN" lognormal and "RIG" reciprocal inverse Gaussian, DiracDU, binomial and discrete triangular; see Kokonendji and Senga Kiessé (2011), and also Kokonendji et al. (2009).

Usage

hcvreg.fun(Vec, ...)
## Default S3 method:
hcvreg.fun(Vec, y, type_data = c("discrete", "continuous"), 
ker = c("bino", "triang", "dirDU", "BE", "GA", "LN", "RIG"),
 h = NULL, a0 = 0, a1 = 1, a = 1, c = 2, ...)

Arguments

Vec

The explanatory variable.

y

The response variable.

type_data

The data sample type. Data can be continuous or discrete.

ker

A character string giving the smoothing kernel to be used which is the associated kernel: "BE" extended beta, "GA" gamma, "LN" lognormal and "RIG" reciprocal inverse Gaussian, "dirDU" DiracDU,"bino" binomial, "triang" discrete triangular.

h

The bandwidth or smoothing parameter.the smoothing bandwidth to be used, can also be a character string giving a rule to choose the bandwidth.

a0

The left bound of the support used for extended beta kernel. Default value is 0 for beta kernel.

a1

The right bound of the support used for extended beta kernel. Default value is 1 for beta kernel.

a

The arm of the discrete triangular kernel

c

The number of categories

...

Further arguments

Details

The selection of the bandwidth parameter is always crucial. If the bandwidth is small, we will obtain an undersmoothed estimator, with high variability. On the contrary, if the value is big, the resulting estimator will be very smooth and farther from the function that we are trying to estimate. The cross-validation function defined in the above sections is used to compute the optimal bandwidth for the associated kernels.

Value

Returns a list containing:

kernel

The associated kernel used to compute the optimal bandwidth.

hcv

The optimal bandwidth parameter obtained by cross-validation.

CV

The values of the cross-validation.

seq_bws

A sequence of bandwidths where the cross-validation is computed.

Author(s)

W. E. Wansouwé, S. M. Somé and C. C. Kokonendji

References

Kokonendji, C.C. and Senga Kiessé, T. (2011). Discrete associated kernel method and extensions, Statistical Methodology 8, 497 - 516.

Kokonendji, C.C., Senga Kiessé, T. and Demétrio, C.G.B. (2009). Appropriate kernel regression on a count explanatory variable and applications, Advances and Applications in Statistics 12, 99 - 125.

Examples

## Data can be simulated data or real data
## We use real data 
## and then compute the cross validation. 
data(milk)
x=milk$week
y=milk$yield
hcvreg.fun(x,y,"discrete",ker="triang",a=1)