R Under development (unstable) (2024-02-22 r85974 ucrt) -- "Unsuffered Consequences"
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> 
> library(OneStep)
Loading required package: fitdistrplus
Loading required package: MASS
Loading required package: survival
Loading required package: numDeriv
Loading required package: parallel
Loading required package: extraDistr
> 
> n <- 200
> theta <- c(0.5, 1.5)
> 
> M <- 100
> M <- 10
> 
> f <- function()
+ {
+   o.sample <- rbeta(n, shape1=theta[1], shape2=theta[2])
+   benchonestep(o.sample,  "beta",  methods=c("mle",  "mme",  "onestep")) 
+ }  
> 
> resall <- replicate(M,  f())  
>   
> tabMLE <- resall[1:2, "mle", ]
> tabME <- resall[1:2, "mme", ]
> tabLCE <- resall[1:2, "onestep", ]
> 
> 
> ###Visualisation et Information de Fisher
> 
> res <- sqrt(n)*(tabMLE-matrix(rep(theta, M), 2, M))
> res2 <- sqrt(n)*(tabME-matrix(rep(theta, M), 2, M))
> res3 <- sqrt(n)*(tabLCE-matrix(rep(theta, M), 2, M))
> 
> 
> tabtime <- t(resall[3, , ])
> 
> 
> FisherInfo <- matrix(0, 2, 2)
> FisherInfo[1, 1] <- trigamma(theta[1]) -trigamma(theta[1]+theta[2])
> FisherInfo[2, 1] <- -trigamma(theta[1]+theta[2])
> FisherInfo[1, 2] <- -trigamma(theta[1]+theta[2])
> FisherInfo[2, 2] <- trigamma(theta[2]) -trigamma(theta[1]+theta[2])
> 
> covlim <- solve(FisherInfo)
> 
> ## Moments variance
> J11 <- theta[2]/(theta[1]+theta[2])^2
> J12 <- -theta[1]/(theta[1]+theta[2])^2
> J21 <- (2*theta[1]^2*theta[2]+2*theta[1]*theta[2]^2+2*theta[1]*theta[2]+theta[2]^2+theta[2])/(theta[1]+theta[2])^2/(theta[1]+theta[2]+1)^2
> J22 <- -theta[1]*(theta[1]+1)*(2*theta[1]+2*theta[2]+1)/(theta[1]+theta[2])^2/(theta[1]+theta[2]+1)^2
> 
> J <- matrix(c(J11, J12, J21, J22), 2, 2, byrow=TRUE)
> 
> A11 <- theta[1]*theta[2]/(theta[1]+theta[2])^2/(theta[1]+theta[2]+1)
> A12 <- 2*theta[2]*theta[1]*(theta[1]+1)/(theta[1]+theta[2])^2/(theta[1]+theta[2]+1)/(theta[1]+theta[2]+2)
> A22 <- theta[1]*(theta[1]+1)*(theta[1]+2)*(theta[1]+3)/(theta[1]+theta[2])/(theta[1]+theta[2]+1)/(theta[1]+theta[2]+2)/(theta[1]+theta[2]+3)-theta[1]^2*(theta[1]+1)^2/(theta[1]+theta[2])^2/(theta[1]+theta[2]+1)^2
> 
> 
> A <- matrix(c(A11, A12, A12, A22), 2, 2, byrow=TRUE)
> Jinv <- solve(J)
> Sigma <- Jinv%*%A%*%t(Jinv)
> 
> 
> layout(matrix(1:6, 2, 3, byrow=TRUE))
> hist(res[1, ], freq=FALSE, nclass=40, xlim=c(-3, 3), ylim=c(0, 0.8), main="MLE theta1", xlab="")
> x <- seq(-3, 3, length=100)
> y <- dnorm(x, mean=0, sd=sqrt(covlim[1, 1]))
> lines(x, y, col="red")
> hist(res2[1, ], freq=FALSE, nclass=40, xlim=c(-3, 3), ylim=c(0, 0.8), main="ME theta1", xlab="")
> lines(x, y, col="red")
> y2 <- dnorm(x, mean=0, sd=sqrt(Sigma[1, 1]))
> lines(x, y2, col="blue")
> hist(res3[1, ], freq=FALSE, nclass=40, xlim=c(-3, 3), ylim=c(0, 0.8), main="LCE theta1", xlab="")
> lines(x, y, col="red")
> 
> hist(res[2, ], freq=FALSE, nclass=40, xlim=c(-8, 8), ylim=c(0, 0.25), main="MLE theta2", xlab="")
> x <- seq(-10, 10, length=100)
> y <- dnorm(x, mean=0, sd=sqrt(covlim[2, 2]))
> lines(x, y, col="red")
> hist(res2[2, ], freq=FALSE, nclass=40, xlim=c(-8, 8), ylim=c(0, 0.25), main="ME theta2", xlab="")
> lines(x, y, col="red")
> y2 <- dnorm(x, mean=0, sd=sqrt(Sigma[2, 2]))
> lines(x, y2, col="blue")
> hist(res3[2, ], freq=FALSE, nclass=40, xlim=c(-8, 8), ylim=c(0, 0.25), main="LCE theta2", xlab="")
> y <- dnorm(x, mean=0, sd=sqrt(covlim[2, 2]))
> lines(x, y, col="red")
> 
> 
> 
> proc.time()
   user  system elapsed 
   0.96    0.21    1.18