l2d: L^2 inner product of estimated probability densities

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/l2d.R

Description

Computes the L^2 inner product of multivariate probability densities, estimated from samples.

Usage

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l2d(x1, x2, method = "gaussiand", check = FALSE, varw1, varw2)

Arguments

x1

a matrix or data frame of n1 rows (observations) and p columns (variables) or a vector of length n1.

x2

matrix or data frame of n2 rows and p columns or vector of length n1.

method

string. It can be:

  • "gaussiand" if the densities are considered to be Gaussian.

  • "kern" if they are estimated using the Gaussian kernel method.

check

logical. When TRUE (the default is FALSE) the function checks if the smoothing bandwidth matrices are not degenerate, before computing the inner product.

varw1, varw2

a p \times p-symmetric matrix: the smoothing bandwidth for the estimation of the probability densities. If they are omitted, the smoothing bandwidth are computed using the normal reference rule matrix bandwidth (see details).

Details

Value

Returns the L^2 inner product of the two probability densities. Be careful! If check = FALSE and one smoothing bandwidth matrix is degenerate, the result returned can not be considered.

Author(s)

Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Gilles Hunault, Sabine Demotes-Mainard

References

Boumaza, R., Yousfi, S., Demotes-Mainard, S. (2015). Interpreting the principal component analysis of multivariate density functions. Communications in Statistics - Theory and Methods, 44 (16), 3321-3339.

Wand, M., Jones, M. (1995). Kernel smoothing. Chapman and Hall/CRC, London.

Yousfi, S., Boumaza R., Aissani, D., Adjabi, S. (2014). Optimal bandwith matrices in functional principal component analysis of density functions. Journal of Statistical Computational and Simulation, 85 (11), 2315-2330.

See Also

l2dpar for Gaussian densities, the parameters being given.

Examples

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require(MASS)
m1 <- c(0,0)
v1 <- matrix(c(1,0,0,1),ncol = 2) 
m2 <- c(0,1)
v2 <- matrix(c(4,1,1,9),ncol = 2)
x1 <- mvrnorm(n = 3,mu = m1,Sigma = v1)
x2 <- mvrnorm(n = 5, mu = m2, Sigma = v2)
l2d(x1, x2, method = "gaussiand")
l2d(x1, x2, method = "kern")
l2d(x1, x2, method = "kern", varw1 = v1, varw2 = v2)

dad documentation built on Sept. 2, 2017, 1:04 a.m.