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# One-Step Estimation Approach:
# find a suitable starting point
# and then search for a root of the
# quasi-score by fisher scoring.
library(qle)
data(normal)
# starting point
x0 <- c("mu"=3,"sigma"=2.5)
# box constraints for parameters
lower <- qsd$lower
upper <- qsd$upper
## use log average approximation
## of variance matrix as an interpolation
qsd$var.type <- "logMean"
# direct minimization of Mahalanobis distance
ctls <- list("stopval"=1e-10,"maxeval"=1000)
## Using `nloptr`directly,
## though quite slow but possible
S0 <- nloptr::direct("mahalDist",
lower=lower,
upper=upper,
control=ctls,
qsd=qsd, value.only=TRUE)
print(S0)
## A least squares approach to find suitable
## starting point, if possible, by a global
# search strategy called `direct` (see nloptr::direct).
W <- diag(1,2)
qsd$criterion <- "mahal"
# one-step minimization
S1 <- searchMinimizer(x0, qsd, W=W, method="direct",
control=list("stopval"=1e-3), verbose=TRUE)
# results
print(S1)
## now apply quasi-likelihood with quasi-scoring
qsd$criterion <- "qle"
qscoring(qsd, S1$par)
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