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example.GMM <- function(){
## General data
theta <- c(1.5,0.5,1,0)
pm <- 0
set.seed(345);
x <- rstable(100,theta[1],theta[2],theta[3],theta[4],pm)
##---------------- 2S free ----------------
## method specific arguments
regularization="cut-off"
WeightingMatrix="OptAsym"
alphaReg=0.005
## If you are just interested by the value
## of the 4 estimated parameters
t_scheme="free"
t_seq=seq(0.1,2,length.out=12)
algo = "2SGMM"
suppressWarnings(GMMParametersEstim(x=x,
algo=algo,alphaReg=alphaReg,
regularization=regularization,
WeightingMatrix=WeightingMatrix,
t_scheme=t_scheme,
pm=pm,PrintTime=TRUE,t_free=t_seq))
}
example.ML <- function(){
theta <- c(1.5,0.4,1,0)
pm <- 0
## 50 points does not give accurate estimation
## but it makes estimation fast for installation purposes
## use at least 200 points to get decent results.
set.seed(1333);x <- rstable(50,theta[1],theta[2],theta[3],theta[4],pm)
MLParametersEstim(x=x,pm=pm,PrintTime=TRUE)
}
example.Cgmm <- function(){
## general inputs
theta <- c(1.45,0.55,1,0)
pm <- 0
set.seed(2345);x <- rstable(200,theta[1],theta[2],theta[3],theta[4],pm)
## GMM specific params
alphaReg=0.01
subdivisions=20
randomIntegrationLaw="unif"
IntegrationMethod="Simpson"
IterationControl <- list(NbIter=3,PrintIter=FALSE,RelativeErrMax=1e-2)
## Estimation
CgmmParametersEstim(x=x,type="IT",alphaReg=alphaReg,
subdivisions=subdivisions,
IntegrationMethod=IntegrationMethod,
randomIntegrationLaw=randomIntegrationLaw,
s_min=0,s_max=1,
IterationControl=IterationControl,
pm=pm,PrintTime=TRUE)
}
example.Estim <- function(){
theta <- c(1.45,0.55,1,0)
pm <- 0
set.seed(2345)
x <- rstable(200,theta[1],theta[2],theta[3],theta[4],pm)
## Cgmm specific inputs
alphaReg=0.01
theta0 <- c(1.35,0.45,1,0)
subdivisions=20
randomIntegrationLaw="unif"
IntegrationMethod="Simpson"
## Estim procedure
Estim(EstimMethod="Cgmm",data=x,
ComputeCov=TRUE,HandleError=FALSE,
type="2S",alphaReg=alphaReg,
subdivisions=subdivisions,
IntegrationMethod=IntegrationMethod,
randomIntegrationLaw=randomIntegrationLaw,
s_min=0,s_max=1,theta0=theta0,pm=pm,
PrintTime=TRUE,level=0.92)
}
example.RegSol <- function(){
## Adapted from R examples for Solve
## We compare the result of the regularized sol to the expected solution
hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+")}
K_h8 <- hilbert(8);
r8 <- 1:8
alphaReg_robust<- 1e-4
Sa8_robust <- RegularisedSol(K_h8,alphaReg_robust,r8,"LF")
alphaReg_accurate<- 1e-10
Sa8_accurate <- RegularisedSol(K_h8,alphaReg_accurate,r8,"LF")
## when pre multiplied by K_h8 ,the expected solution is 1:8
## User can check the influence of the choice of alphaReg
list(Sa8_robust,Sa8_accurate)
}
example.Integrate <- function(){
## Define the integrand
f_fct <- function(s,x){sapply(X=x,
FUN=sampleComplexCFMoment,
t=s,theta=theta)
}
f_bar_fct <- function(s,x){Conj(f_fct(s,x))}
## Function specific arguments
theta <- c(1.5,0.5,1,0)
set.seed(345);X=rstable(3,1.5,0.5,1,0)
s_min=0;s_max=2
numberIntegrationPoints=10
randomIntegrationLaw="norm"
IntegrateRandomVectorsProduct(f_fct,X,f_bar_fct,X,s_min,s_max,
numberIntegrationPoints,
"Simpson",randomIntegrationLaw)
}
example.cf <- function(){
## define the parameters
nt <- 10
t <- seq(0.1,3,length.out=nt)
theta <- c(1.5,0.5,1,0)
pm <- 0
## Compute the characteristic function
ComplexCF(t=t,theta=theta,pm=pm)
}
example.jack <- function(){
## define the parameters
nt <- 10
t <- seq(0.1,3,length.out=nt)
theta <- c(1.5,0.5,1,0)
pm <- 0
## Compute the jacobian of the characteristic function
jacobianComplexCF(t=t,theta=theta,pm=pm)
}
example.Kout <- function(){
pm=0
theta <- c(1.45,0.5,1.1,0.4)
set.seed(1235);x <- rstable(500,theta[1],theta[2],theta[3],theta[4],pm=pm)
theta0=theta-0.1
spacing="Kout"
KoutParametersEstim(x=x,theta0=theta0,
spacing=spacing,pm=pm)
}
example.IG <- function(){
x <- rstable(200,1.2,0.5,1,0,pm=0)
IGParametersEstim(x,pm=0)
}
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