bOptEmpProc: Bandwidth Parameter Estimation

Description

In the context of the standard CUSUM test based on the sample mean or in a particular empirical process setting, the following functions estimate the bandwidth parameter controlling the serial dependence when generating dependent multiplier sequences using the 'moving average approach'; see Section 5 of the third reference. The function function bOpt() is called in the functions cpMean(), cpVar(), cpGini(), cpAutocov(), cpCov(), cpTau() and detOpenEndCpMean() when b is set to NULL. The function function bOptEmpProc() is called in the functions cpDist(), cpCopula(), cpAutocop(), stDistAutocop() and simClosedEndCpDist() when b is set to NULL.

Usage

bOpt(influ, weights = c("parzen", "bartlett"))
bOptEmpProc(x, m=5, weights = c("parzen", "bartlett"),
            L.method=c("max","median","mean","min"))

Value

A strictly positive integer.

Arguments

influ: a numeric containing the relevant influence coefficients, which, in the case of the standard CUSUM test based on the sample mean, are simply the available observations; see also the last reference.
x: a data matrix whose rows are continuous observations.
weights: a string specifying the kernel for creating the weights used in the generation of dependent multiplier sequences within the 'moving average approach'; see Section 5 of the third reference.
m: a strictly positive integer specifying the number of points of the uniform grid on \((0,1)^d\) (where \(d\) is ncol(x)) involved in the estimation of the bandwidth parameter; see Section 5 of the third reference. The number of points of the grid is given by m^ncol(x) so that m needs to be decreased as \(d\) increases.
L.method: a string specifying how the parameter L involved in the estimation of the bandwidth parameter is computed; see Section 5 of the third reference.

Details

The implemented approach results from an adaptation of the procedure described in the first two references (see also the references therein). The use of theses functions in a context different from that considered in the third or fourth reference may not be meaningful.

Acknowledgment: Part of the code of the function results from an adaptation of R code of C. Parmeter and J. Racine, itself an adaptation of Matlab code by A. Patton.

References

D.N. Politis and H. White (2004), Automatic block-length selection for the dependent bootstrap, Econometric Reviews 23(1), pages 53-70.

D.N. Politis, H. White and A.J. Patton (2004), Correction: Automatic block-length selection for the dependent bootstrap, Econometric Reviews 28(4), pages 372-375.

A. Bücher and I. Kojadinovic (2016), A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing, Bernoulli 22:2, pages 927-968, https://arxiv.org/abs/1306.3930.