Kern.fun: Construction of n x n Kernel Matrices

In estsyawo/bayesprdopt: Useful Functions and Algorithms

Construction of n x n Kernel Matrices

Description

Kern.fun computes the n x n matrix of kernels used in the integrated moment class of estimators.

Usage

Kern.fun(Z, Kern = "Euclid", X = NULL, Y = NULL)

Arguments

Z	n x p matrix of instrumental variables
Kern	type of kernel desired.
X	matrix of endogenous covariates. Ought to be demeaned.
Y	the outcome variable. Ought to be demeaned.

Details

The (i,j)'th elements of available kernel methods are

"Euclid"

Negative of the Euclidean distance between two vectors: -||Z_i-Z_j||

"Gauss.W"

The weighted Gaussian kernel: exp(-0.5(Z_i-Z_j)'V^-1(Z_i-Z_j)) where V is the variance of V

"Gauss"

The unweighted Gaussian kernel: exp(-||Z_i-Z_j||^2)

"DL"

The kernel of Dominguez & Lobato 2004: 1/n\sum{l=1}^n I(Z_i\le Z_l)I(Z_j\le Z_l)

"Esc6"

The projected version of the DL in Escanciano 2006.

"WMD"

The kernel used in Antoine & Lavergne 2014. See page 60 of paper.

"WMDF"

WMD à la Fuller (1977) used in Antoine & Lavergne 2014. See page 64 of paper.

Value

the n\times n kernel matrix

Examples

set.seed(12); X = rnorm(5); Z=cbind(X,abs(X)); Kern.fun(Z,"DL")

estsyawo/bayesprdopt documentation built on April 2, 2024, 2:18 p.m.