tobit_sd_mle {ebTobit}

Maximum Likelihood Estimator for a Single Standard Deviation Parameter

Description

Use standard numerical optimization methods to maximize the log-likelihood of the given problem. If all of the data is passed in, this method computes the global estimate of standard deviation. By passing in a subset of the data, more specific estimates can be made (ex column-specific standard deviations).

Usage

tobit_sd_mle(
  L,
  R,
  mu = matrix(mean(L + R)/2, nrow(L), ncol(L)),
  interval = c(1e-04, 100),
  tol = .Machine$double.eps^0.25
)

Arguments

L

matrix of lower bounds on observations (n x p)

R

matrix of upper bounds on observations (n x p)

mu

matrix of known means (n x p)

interval

a vector containing the end-points of the interval defining the convex search space (default: c(1e-4, 1e+2))

tol

the desired accuracy

Value

a list containing estimate (maximum) and log-likelihood (objective)

Examples

set.seed(1)
n = 100; p = 5; r = 2
U.true = matrix(stats::rexp(n*r), n, r)
V.true = matrix(sample(x = c(1,4,7),
                       size = p*r, 
                       replace = TRUE, 
                       prob = c(0.7, 0.2, 0.1)), 
                p, r)
TH = tcrossprod(U.true, V.true)
X = TH + matrix(stats::rnorm(n*p, sd = 1), n, p)
ldl <- 0.1 # lower detection limit, known to be non-negative
L <- ifelse(X < ldl, 0, X)
R <- ifelse(X < ldl, ldl, X)
tobit_sd_mle(L, R, mu = TH)