Question

我正在尝试编写一个代码来确定g，sigma和lambda，使用以下最大可能性 Function Equation。我需要限制间隔以确保方程式没有采用负数的对数，但是，它出现了错误“L-BFGS-B需要有限值”。我该怎么做才能解决这个问题？

lnQs<- c(0.4452211,  3.2828926,  3.0752400,  2.6613305,  5.8122312,  0.5629881,  0.8445112,  4.4336806,  3.8253957,  0.9336889,  1.5188934,  4.3915304, 2.5368227,  0.3729370,  2.3683679,  2.3555777,  0.5985054,  0.6240360,  0.9462143,  0.5440311,  2.6390102,  0.4921728,  0.2971820,  0.1939826, 0.5621709,  0.7839881,  2.2367834, 10.4101839,  5.8010886,  6.0974008)
Rf<- c(0.0484, 0.0537, 0.0598, 0.0590, 0.0590, 0.0571, 0.0497, 0.0497, 0.0492, 0.0588, 0.0586, 0.0492, 0.0468, 0.0480, 0.0405, 0.0405, 0.0488, 0.0452, 0.0675, 0.0395, 0.0395, 0.0385, 0.0400, 0.0432, 0.0394, 0.0397, 0.0397, 0.0407, 0.0436, 0.0436)
S<- c(0.8,  2.3,  2.2,  3.3,  4.9,  8.7,  0.8,  0.9,  1.8,  2.3,  1.3,  1.9,  5.7,  9.3,  4.9, 18.7,  3.6,  2.4, 15.1, 10.3,  0.8,  2.9, 12.0,  0.8,  9.9,  1.3,  8.9, 12.3,  4.2,  4.2)
T<- c(1.0,  5.0,  5.0,  7.0,  5.1, 21.0, 14.1,  5.0,  5.0, 12.0,  7.0,  3.0,  7.0, 21.0,  7.0, 21.0, 21.0, 21.0, 21.0, 20.0,  5.0, 21.0, 21.0, 21.1, 21.0, 14.0,  12.0, 14.0,  5.0,  5.0)

LL<- function(g,sigma,lambda){
  R=(dnorm(lnQs,(log(1+Rf+lambda)-sigma^2/2)*S-log(((1+Rf+lambda)/(1+g))^T-1),sigma*S^0.5))
#
    -sum(log(R), log=TRUE)
}
fit<-mle(minuslogl=LL, start=list(g=.05, sigma=.2, lambda=.1), method = "L-BFGS-B",lower=c(0,0,0.0915),upper=c(0.13,Inf,Inf))
summary(fit)
#Criteria required 
#   lambda>-(1+Rf)  - easily done with restriction lambda>0
#   lambda>(g-Rf)   - NOT SURE HOW TO DEAL WITH lowest Rf=0.0385, tried putting upper limit on g and lower limit on lambda for now
#   sigma>0         - easily done with restriction sigma>0
#   Problem that L-BFGS-B needs finite values offit<-mle(minuslogl=LL, start=list(g=.077, sigma=.256, lambda=.110), method = "BFGS")

Answer 1

您是否需要MLE的sigma和lambda参数的Inf限制？例如，以下工作没有错误（虽然lambda估计非常糟糕，高std错误）：

set.seed(123)
T<-0.5
S<-1
Rf<-2
g <-.1 
sigma <- .5
lambda <- 1
lnQs <- rnorm(100,(log(1+Rf+lambda)-sigma^2/2)*S-log(((1+Rf+lambda)/(1+g))^T-1),sigma*S^0.5)

# negative ll fn  
LL<- function(g,sigma,lambda){
  R <- dnorm(lnQs,(log(1+Rf+lambda)-sigma^2/2)*S-log(((1+Rf+lambda)/(1+g))^T-1),sigma*S^0.5)
  -sum(log(R))
}
fit<-mle(minuslogl=LL, start=list(g=.05, sigma=.2, lambda=.1), method = "L-BFGS-B",lower=c(0,0,0.0915),upper=c(0.13,5,5))
summary(fit)
Maximum likelihood estimation

Call:
mle(minuslogl = LL, start = list(g = 0.05, sigma = 0.2, lambda = 0.1), 
    method = "L-BFGS-B", lower = c(0, 0, 0.0915), upper = c(0.13, 
        5, 5))

Coefficients:
       Estimate Std. Error
g       0.10583  16.869598
sigma   0.45412   0.032111
lambda  0.39076 363.867321

使用您提供的数据，LL在许多点处使用许多不同的参数值评估无穷大，例如在[0,1] x [0,1] x [0,1]上使用简单的网格搜索您可以找到LL评估为无穷大的有以下几点（有时也是NAN），这就是L-BFGS-G失败的原因：

g <- seq(0,1,length=10)
sigma <- seq(0,1,length=10)
lambda <- seq(0,1,length=10)
# grid search
for (i in 1:10) {
  for (j in 1:10) {
    for (k in 1:10) {
      if (LL(g[i],sigma[j],lambda[k]) == Inf) {
        print(paste(g[i],sigma[j],lambda[k]))
      }
    }
  }
}

LL评估为Inf

的一些要点

[1] "0 0 0"
[1] "0 0 0.111111111111111"
[1] "0 0 0.222222222222222"
[1] "0 0 0.333333333333333"
[1] "0 0 0.444444444444444"
[1] "0 0 0.555555555555556"
[1] "0 0 0.666666666666667"
[1] "0 0 0.777777777777778"
[1] "0 0 0.888888888888889"
[1] "0 0 1"
[1] "0 0.111111111111111 0.111111111111111"
[1] "0 0.111111111111111 0.222222222222222"
[1] "0 0.111111111111111 0.333333333333333"
[1] "0 0.111111111111111 0.444444444444444"

有一个简单的黑客可以解决问题：

LL<- function(g,sigma,lambda){
      R=(dnorm(lnQs,(log(1+Rf+lambda)-sigma^2/2)*S-log(((1+Rf+lambda)/(1+g))^T-1),sigma*S^0.5))
      #
      ll <- -sum(log(R), log=TRUE)
      ifelse(ll == Inf, 9999999, ll) # return a large enough number if Inf
}

fit<-mle(minuslogl=LL, start=list(g=.05, sigma=.2, lambda=.1), method = "L-BFGS-B",lower=c(0,0,0.0915),upper=c(0.13,Inf,Inf))
summary(fit)


Maximum likelihood estimation

Call:
mle(minuslogl = LL, start = list(g = 0.05, sigma = 0.2, lambda = 0.1), 
    method = "L-BFGS-B", lower = c(0, 0, 0.0915), upper = c(0.13, 
        Inf, Inf))

Coefficients:
        Estimate Std. Error
g      0.1249300 0.07295480
sigma  0.8795551 0.07349924
lambda 0.0915000 0.07459289

-2 log L: 160.1491

多变量非线性正态分布的最大似然

1 个答案: