getLamb {gmm} | R Documentation |
It computes the vector of Lagrange multipliers, which maximizes the GEL objective function, using an iterative Newton method.
getLamb(gt, l0, type = c("EL","ET","CUE", "ETEL", "HD","ETHD","RCUE"), tol_lam = 1e-7, maxiterlam = 100, tol_obj = 1e-7, k = 1, method = c("nlminb", "optim", "iter", "Wu"), control = list())
gt |
A n \times q matrix with typical element g_i(θ,x_t) |
l0 |
Vector of starting values for lambda |
type |
"EL" for empirical likelihood, "ET" for exponential tilting, "CUE" for continuous updated estimator, and "HD" for Hellinger Distance. See details for "ETEL" and "ETHD". "RCUE" is a restricted version of "CUE" in which the probabilities are bounded below by zero. In that case, an analytical Kuhn-Tucker method is used to find the solution. |
tol_lam |
Tolerance for λ between two iterations. The
algorithm stops when \|λ_i -λ_{i-1}\| reaches
|
maxiterlam |
The algorithm stops if there is no convergence after "maxiterlam" iterations. |
tol_obj |
Tolerance for the gradiant of the objective function. The
algorithm returns a non-convergence message if \max(|gradiant|)
does not reach |
k |
It represents the ratio k1/k2, where k1=\int_{-∞}^{∞} k(s)ds and k2=\int_{-∞}^{∞} k(s)^2 ds. See Smith(2004). |
method |
The iterative procedure uses a Newton method for solving
the FOC. It i however recommended to use |
control |
Controls to send to |
It solves
the problem \max_{λ} \frac{1}{n}∑_{t=1}^n
ρ(gt'λ). For the type "ETEL", it is only used by
gel
. In that case λ is obtained by maximizing
\frac{1}{n}∑_{t=1}^n ρ(gt'λ), using
ρ(v)=-\exp{v} (so ET) and θ by minimizing the same
equation but with ρ(v)-\log{(1-v)}. To avoid NA's,
constrOptim
is used with the restriction λ'g_t
< 1. The type "ETHD" is experimental and proposed by Antoine-Dovonon
(2015). The paper is not yet available.
lambda: A q\times 1 vector of Lagrange multipliers which solve the system of equations given above.
conv
: Details on the type of convergence.
Newey, W.K. and Smith, R.J. (2004), Higher Order Properties of GMM and Generalized Empirical Likelihood Estimators. Econometrica, 72, 219-255.
Smith, R.J. (2004), GEL Criteria for Moment Condition Models. Working paper, CEMMAP.
Wu, C. (2005), Algorithms and R codes for the pseudo empirical likelihood method in survey sampling. Survey Methodology, 31(2), page 239.
g <- function(tet,x) { n <- nrow(x) u <- (x[7:n] - tet[1] - tet[2]*x[6:(n-1)] - tet[3]*x[5:(n-2)]) f <- cbind(u, u*x[4:(n-3)], u*x[3:(n-4)], u*x[2:(n-5)], u*x[1:(n-6)]) return(f) } n = 500 phi<-c(.2, .7) thet <- 0.2 sd <- .2 x <- matrix(arima.sim(n = n, list(order = c(2, 0, 1), ar = phi, ma = thet, sd = sd)), ncol = 1) gt <- g(c(0,phi),x) getLamb(gt, type = "EL",method="optim")