lambdasearch {KRLS}

Leave-one-out optimization to find \lambda

Description

Function conducts leave-one-out optimization to find \lambda using a golden search search with caching. This function is called internally by krls. It would normally not be called by the user directly.

Usage

lambdasearch(L=NULL,
           U=NULL,
           y=NULL,
           Eigenobject=NULL,
           tol=NULL,
           noisy=FALSE,
           eigtrunc=NULL)

Arguments

L

Non-negative scalar that determines the lower bound of the search window. Default is NULL which means that the lower bound is found using an algorithm (see details).

U

Positive scalar that determines the upper bound of the search window. Default is NULL which means that the upper bound is found using an algorithm (see details).

y

N by 1 matrix of outcomes.

Eigenobject

List that contains the eigenvalues and eigenvectors of the kernel matrix K.

tol

Positive scalar that determines the tolerance used in the optimization routine used to find \lambda. Default is NULL which means that convergence is achieved when the difference in the sum of squared leave-one-out errors between the i and the i+1 iteration is less than N * 10^-3.

noisy

If TRUE, the function will print details of the golden section search.

eigtrunc

Positive scalar value that determines truncation of eigenvalues for lamnda search window. See krls for details. Default is NULL which means no truncation.

Details

By default, upper bound is found as follows: Set j to n, decrease by one until the following is longer true: sum(EigenValues / (EigenValues + j)) < 1.

By default, upper bound is found as follows: Get the position, q, of the eigenvalue that is closest to max(Eigenvalue)/1000. Set j to 0, increase in steps of 0.05 until the below is longer true: sum(EigenValues / (EigenValues + j)) > q.

Value

A scalar that contains the \lambda that minimizes the sum of squared leave-one-out errors.

Author(s)

Jens Hainmueller (Stanford) and Chad Hazlett (MIT)

See Also

krls