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findU2d <- function(NPmle, ConfInt, LogLikfn, Pfun, dataMat, level=3.84)
{
#### If saving memory space is not the top priority, and search 10 by 10 trials are OK, this is the function.
#### NPmle: should be a vector of length 2, they are the NPmle of beta1 and beta2.
#### ConfInt: should be a vector of length 2 ... the aprox. length of two 90% confidence intervals
#### for beta1, beta2. They do not have to be exact. But they provides good initial step.
#### LogLikfn: is a function that takes two inputs: para + dataMat, and returns the loglik value.
#### Pfun: is a function of 2 NPmle. Pfun(beta1, beta2) = parameter we want to find confidence Interval.
#### dataMat: is only used for the function LogLikfn( ).
####
#### Output: The beta1 and beta2, and Pfun which is maxed inside 95 percent contour. and Loglik value.
temp0 <- LogLikfn(mle=NPmle, dataMat)
MaxValue <- temp0$Loglik
PfunUold <- Pfun(NPmle[1], NPmle[2])
stepsize <- ConfInt/3
b1vec <- NPmle[1] + stepsize[1] * (1:10 - 5.5) ### pertubations, 10 by 10 or others.
b2vec <- NPmle[2] + stepsize[2] * (1:10 - 5.5)
temp <- matrix(NA, nrow = 4, ncol = 100)
temp[1, ] <- rep(b1vec, each=10)
temp[2, ] <- rep(b2vec, times=10)
for (i in 1:10) for (j in 1:10) {
ind <- (i - 1) * 10 + j
temp[4, ind] <- LogLikfn(mle=c(b1vec[i],b2vec[j]),dataMat)$Loglik
#### temp[3, ind] <- Pfun(b1vec[i], bevec[j]) #### Or other fun??
}
subsetInd <- (temp[4, ] >= (MaxValue - level/2))
ParaTrials <- temp[, subsetInd]
TrialValues <- Pfun( ParaTrials[1,], ParaTrials[2,] )
#### TrialValues <- ParaTrials[3,]
maxInd <- which.max(TrialValues)
PfunU <- TrialValues[maxInd]
maxParaOLD <- maxPara <- ParaTrials[, maxInd]
print(c(PfunU, maxPara))
for (N in 1:25){ #### may be more steps?
if( sum(subsetInd) < 20) stepsize <- stepsize/2
#### if( abs(Ub1 - mean(b1vec)) < 4*min(stepsize) ) stepsize <- stepsize/2 ####
if(PfunU <= PfunUold) {maxpara <- maxParaOLD ; stepsize <- stepsize/4}
b1vec <- maxPara[1] + stepsize[1]*(1:10 - 5.5)
b2vec <- maxPara[2] + stepsize[2]*(1:10 - 5.5)
temp[1, ] <- rep(b1vec, each=10)
temp[2, ] <- rep(b2vec, times=10)
for (i in 1:10) for (j in 1:10) {
ind <- (i-1)*10 + j
temp[4, ind] <- LogLikfn(mle=c(b1vec[i], b2vec[j]), dataMat)$Loglik
#### temp[3, ind] <- Pfun(b1vec[i], b2vec[j])
}
subsetInd <- (temp[4, ] >= (MaxValue - level/2))
ParaTrials <- temp[, subsetInd]
TrialValues <- Pfun( ParaTrials[1,], ParaTrials[2,] )
#### TrialValues <- ParaTrials[3,]
maxInd <- which.max(TrialValues)
PfunUold <- PfunU
PfunU <- TrialValues[maxInd]
maxPara <- ParaTrials[, maxInd]
print(c(PfunU, maxPara))
}
list(Upper = PfunU, maxParameterNloglik = maxPara)
}
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