wmonfromx {EbayesThresh}

Find monotone Empirical Bayes weights from data.

Description

Given a vector of data, find the marginal maximum likelihood choice of weight sequence subject to the constraints that the weights are monotone decreasing.

Usage

wmonfromx(xd, prior = "laplace", a = 0.5, tol = 1e-08, maxits = 20)

Arguments

xd

A vector of data.

prior

Specification of the prior to be used; can be cauchy or laplace.

a

Scale parameter in prior if prior="laplace". Ignored if prior="cauchy".

tol

Absolute tolerance to within which estimates are calculated.

maxits

Maximum number of weighted least squares iterations within the calculation.

Details

The weights is found by marginal maximum likelihood. The search is over weights corresponding to thresholds in the range [0, \sqrt{2 \log n}], where n is the length of the data vector.

An iterated least squares monotone regression algorithm is used to maximize the log likelihood. The weighted least squares monotone regression routine isotone is used.

To turn the weights into thresholds, use the routine tfromw; to process the data with these thresholds, use the routine threshld.

Value

The vector of estimated weights is returned.

Author(s)

Bernard Silverman

References

See ebayesthresh and http://www.bernardsilverman.com

See Also

wfromx, isotone