R 高斯牛顿法

求非线性分布的最大似然估计（在R中，使用高斯-牛顿法）：

为此，我被要求生成一些从0均匀（随机）分布的数据

y = sin(x*theta) + epsilon
where epsilon ~ N(0 , 0.01^2)

theta <- 2

x <- runif(200, 0, 10)

x <- sort(x)  #this is just to sort the generated data so that plotting it
 #actually looks like a sine funciton

y <- sin(x*theta) + rnorm(200, mean = 0, sd = 0.1^2)

GN_sin <- function(theta.iter, x , y, epsilon){

 index <- TRUE

 while (index){

     y.iter <- matrix(y - sin(x*theta.iter), 200, 1)

     x.iter <- matrix(theta.iter*cos(x*theta.iter), 200, 1)

     theta.new <- theta.iter +

         solve(t(x.iter)%*%x.iter)%*%t(x.iter)%*%y.iter

         if (abs(theta.new-theta.iter) < epsilon) {index <- FALSE}

   theta.iter <- as.vector(theta.new)

 cat(theta.iter, '\n')

 }
}