A brief summary of the results

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Description

For a given data sample, the function gives a summary of the results of five computed values: p.m.f. f_0, estimated values \tilde{f}_n, ISE_0, normalizing constant C_n and smoothing parameter h; see Kokonendji and Senga Kiessé (2011), and also Zougab et al. (2012).

Usage

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sumry(Vec,type_bw, ker = "bino", h = NULL,  a = 1, c = 2)

Arguments

Vec

The data sample.

ker

The kernel function: "dirDU" DiracDU,"bino" Binomial, "triang" Discrete Triangular.

h

The bandwidth or smoothing parameter. If NULL,it is calculated depending on the value of type_bw.

type_bw

The technique of bandwidth selection: Bayesian or cross-validation.

a

The arm in the Discrete Triangular kernel.

c

The number of categories in DiracDU.

Value

Returns a list containing:

n

The number of observations.

support_of_f_n

The support of the p.m.f. fn.

f_0

The couples (x,f0(x)).

f_n

The couples (x,fn(x)).

ISE_0

The integrated square error.

C_n

The normalizing constant.

h

The bandwith parameter used to compute fn.

Author(s)

W. E. Wansouwé, C. C. Kokonendji and D. T. Kolyang

References

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

Zougab, N., Adjabi, S. and Kokonendji, C.C. (2012). Binomial kernel and Bayes local bandwidth in discrete functions estimation. Journal of Nonparametric Statistics 24, 783 - 795.

Examples

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## A sample data with n=60.
V<-c(10,0,1,0,4,0,6,0,0,0,1,1,1,2,4,4,5,6,6,6,6,7,1,7,0,7,7,
7,8,0,8,12,8,8,9,9,0,9,9,10,10,10,10,0,10,10,11,12,12,10,12,12,
13,14,15,16,16,17,0,12)

sumry(V,type_bw="CV")