Estimating equation for the geometric mean

Returns a 1-by-n matrix of estimating equation contributions for the geometric mean. When log_theta = TRUE (default), solves \(\log(Y_i) - \log(\theta)\). When log_theta = FALSE, solves \(\log(Y_i) - \theta\) where \(\theta\) is the log of the geometric mean.

Usage

ee_mean_geometric(theta, y, weights = NULL, log_theta = TRUE)

Arguments

theta

Numeric vector of length 1.

y

Numeric vector of positive observed values.

weights

Optional numeric vector of weights. Default NULL.

log_theta

Logical. If TRUE (default), internally log-transforms theta. Default TRUE.

Value

A 1-by-n matrix.

Examples

y <- c(1, 2, 3, 1, 4, 5, 3, 2, 6, 7)
psi <- function(theta) ee_mean_geometric(theta, y = y)
m <- m_estimate(stacked_equations = psi, init = 1)
coef(m)
#>  theta_1 
#> 2.805809