bwd.nrd {etasFLP}

Silverman's rule optimal for the estimation of a kernel bandwidth

Description

Computes the optimal bandwidth with the Silverman's rule of thumb, to be used for a kernel estimator with given points and weights.

Usage

bwd.nrd(x, w=replicate(length(x),1), d = 2)

Arguments

x

numeric vector: sample points to be used for a normal kernel estimator.

w

numeric vector of the same length of x: weights to give to the elements of x. Default is a vector of ones

d

number of dimensions of the kernel estimator.

Details

Computes the optimal bandwidth with the Silverman rule, for a kernel estimator with points x and weights w. If a multivariate kernel is used, (i.e. d > 1), bwd.nrd must be called for each variable. It computes dispersion only with the weighted standard deviation, with no robust alternative. Called by kde2dnew.fortran.

Value

The value of the bandwidth for a sample x and weights w.

Note

It is used in connection with the the declustering method of etasFLP. Points with an higher probability of being part of the background seismicity will weight more in the estimation of the background seismicity.

Note

This is a slight modification of bw.nrd.

Author(s)

Marcello Chiodi

References

Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall: London.

Examples

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