matdistl2d function

Matrix of $L^2$ distances between probability densities

Computes the matrix of the $L^2$ distances between several multivariate ($p > 1$) or univariate ($p = 1$) probability densities, estimated from samples.

matdistl2d(x, method = "gaussiand", varwL = NULL)

Arguments

• x: object of class "folder" containing the data. Its elements have only numeric variables (observations of the probability densities). If there are non numeric variables, there is an error.

• method: string. It can be:

  • "gaussiand" if the densities are considered to be Gaussian.
  • "kern" if they are estimated using the Gaussian kernel method.

• varwL: list of matrices. The smoothing bandwidths for the estimation of each probability density. If they are omitted, the smoothing bandwidths are computed using the normal reference rule matrix bandwidth (see details of the l2d function).

Returns

Positive symmetric matrix whose order is equal to the number of densities, consisting of the pairwise distances between the probability densities.

Author(s)

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

See Also

distl2d.

matdistl2dpar when the probability densities are Gaussian, given the parameters (means and variances).

Examples

data(roses)
    
    # Multivariate:
    X <- as.folder(roses[,c("Sha","Den","Sym","rose")], groups = "rose")
    summary(X)
    mean.X <- mean(X)
    var.X <- var.folder(X)
    
    # Parametrically estimated Gaussian densities:
    matdistl2d(X)
    
    ## Not run:

    # Estimated densities using the Gaussian kernel method ()normal reference rule bandwidth):
    matdistl2d(X, method = "kern")   

    # Estimated densities using the Gaussian kernel method (bandwidth provided):
    matdistl2d(X, method = "kern", varwL = var.X)
## End(Not run)

    # Univariate :
    X1 <- as.folder(roses[,c("Sha","rose")], groups = "rose")
    summary(X1)
    mean.X1 <- mean(X1)
    var.X1 <- var.folder(X1)
    
    # Parametrically estimated Gaussian densities:
    matdistl2d(X1)
    
    # Estimated densities using the Gaussian kernel method (normal reference rule bandwidth):
    matdistl2d(X1, method = "kern")
    
    # Estimated densities using the Gaussian kernel method (normal reference rule bandwidth):
    matdistl2d(X1, method = "kern", varwL = var.X1)