A $n\times q$ matrix with typical element $(t,i)$, $g_i(\theta,x_t)$
lamb
A $q \times 1$ vector of lagrange multipliers
derive
0 for the objective function, 1 for the first derivative with respect to $\lambda$ and 2 for the second derivative with respect to $\lambda$.
type
"EL" for empirical likelihood, "ET" for exponential tilting and "CUE" for continuous updated estimator.
drop
Because the solution may not be in the domain of $\rho(v)$ $\forall t$ in small sample, we can drop those observations to avoid the return of NaN
Value
'rho' returns a scalar if "derive=0", a $q\time 1$ vector if "derive" = 1 and a $q\times q$ matrix if derive = 2.
Details
The objective function is $\frac{1}{n}\sum_{t=1}^n \rho()$, where $\rho(v)=\log{(1-v)}$ for empirical likelihood, $-e^v$ for exponential tilting and $(-v-0.5v^2)$ for continuous updated estimator.
References
Newey, W.K. and Smith, R.J. (2004), Higher Order Properties of GMM and
Generalized Empirical Likelihood Estimators. Econometrica, 72, 219-255.
Hansen, L.P. and Heaton, J. and Yaron, A.(1996),
Finit-Sample Properties of Some Alternative GMM Estimators.
Journal of Business and Economic Statistics, 14
262-280.