Frank copula参数最小化

Question

我正在尝试计算肯德尔的tau给出的Frank copula参数。这是我试图在R中以数字方式解决的问题：

到目前为止，这是我的代码：

copula <- function(tau, method = c("clayton", "gumbel", "frank")){
  if(method == "clayton"){
    tmp <- (2*tau)/(1-tau)
  } else if(method == "gumbel"){
    tmp <- 1/(1-tau)
  } else if(method == "frank"){
    integrand <- function(t) {t/(exp(t)-1)}
    frank_fn <- function(theta) {(((tau - 1)/4) - (((integrate(integrand, 0, theta)[1]/theta) - 1)/theta))^2}
    tmp <- optim(frank_fn, 4, method = "BFGS")
  } else{
    tmp <- "Error: Choice of method is undefined."
  }
  return(tmp)
}

此功能适用于clayton和gumbel但不坦率。它会引发以下错误：

Error in optim(frank_fn, 4, method = "BFGS") : 
  cannot coerce type 'closure' to vector of type 'double'

有人可以帮助解释我的代码有什么问题吗？我对R中的数值优化问题相当新。

更新：

正确的代码如下：

copula <- function(tau, method = c("clayton", "gumbel", "frank")){
  if(method == "clayton"){
    tmp <- (2*tau)/(1-tau)
  } else if(method == "gumbel"){
    tmp <- 1/(1-tau)
  } else if(method == "frank"){
    integrand <- function(t) {t/(exp(t)-1)}
    frank_fn <- function(theta) {(((tau - 1)/4) - ((((integrate(integrand, 0, theta)$value)/theta) - 1)/theta))^2}
    tmp <- optim(4, frank_fn, method = "BFGS")
  } else{
    tmp <- "Error: Choice of method is undefined."
  }
  return(tmp)
}

Answer 1

您在集成方面需要$ value吗？

copula <- function(tau, method = c("clayton", "gumbel", "frank")){
  if(method == "clayton"){
    tmp <- (2*tau)/(1-tau)
  } else if(method == "gumbel"){
    tmp <- 1/(1-tau)
  } else if(method == "frank"){
    integrand <- function(t) {t/(exp(t)-1)}
    frank_fn <- function(theta) {(((tau - 1)/4) - (((integrate(integrand, 0, theta)[1]/theta)$value - 1)/theta))^2}
    tmp <- optim(frank_fn, 4, method = "BFGS")
  } else{
    tmp <- "Error: Choice of method is undefined."
  }
  return(tmp)
}
copula(30,method='clayton')