wfromx {EbayesThresh} | R Documentation |
Suppose the vector (x_1, ..., x_n) is such that x_i is drawn independently from a normal distribution with mean theta_i and variance 1. The prior distribution of the theta_i is a mixture with probability 1-w of zero and probability w of a given symmetric heavy-tailed distribution. This routine finds the marginal maximum likelihood estimate of the parameter w.
wfromx(x, prior = "laplace", a = 0.5)
x |
vector of data |
prior |
specification of prior to be used; can be "cauchy" or "laplace" |
a |
scale factor if Laplace prior is used. Ignored if Cauchy prior is used. |
The weight 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.
The search is by binary search for a solution to the equation S(w)=0, where S is the derivative of the log likelihood. The binary search is on a logarithmic scale in w.
If the Laplace prior is used, the scale parameter is fixed at the value given for a
, and
defaults to 0.5 if no value is provided. To estimate a
as well as w
by marginal
maximum likelihood, use the routine wandafromx
.
The numerical value of the estimated weight.
Bernard Silverman
See ebayesthresh
and http://www.bernardsilverman.com
wandafromx
, tfromx
, tfromw
, wfromt
wfromx(x=rnorm(100, c( rep(0,90), rep(5,10))), prior="cauchy")