The algorithms finds the vector or Lagrange multipliers that maximizes the GEL objective function for a given vector of coefficient \(\theta\).
Wu_lam(gmat, tol=1e-8, maxiter=50, k=1)EEL_lam(gmat, k=1)
REEL_lam(gmat, tol=NULL, maxiter=50, k=1)
ETXX_lam(gmat, lambda0, k, gelType, algo, method, control)
getLambda(gmat, lambda0=NULL, gelType=NULL, rhoFct=NULL,
tol = 1e-07, maxiter = 100, k = 1, method="BFGS",
algo = c("nlminb", "optim", "Wu"), control = list(),
restrictedLam=integer())
It returns the vector \(\rho(gmat \lambda)\) when derive=0,
\(\rho'(gmat \lambda)\) when derive=1 and \(\rho''(gmat
\lambda)\) when derive=2.
The \(n \times q\) matrix of moments
The \(q \times 1\) vector of starting values for the Lagrange multipliers.
A tolerance level for the stopping rule in the Wu algorithm
The maximum number of iteration in the Wu algorithm
A character string specifying the type of GEL. The
available types are "EL", "ET", "EEL",
"HD" and "REEL". For the latter, the algorithm restricts the
implied probabilities to be non negative.
An optional function that return \(\rho(v)\). This is
for users who want a GEL model that is not built in the package. The
four arguments of the function must be "gmat", the matrix of
moments, "lambda", the vector of Lagrange multipliers,
"derive", which specify the order of derivative to return, and
k a numeric scale factor required for time series and kernel
smoothed moments.
A numeric scaling factor that is required when "gmat" is
a matrix of time series which require smoothing. The value depends on
the kernel and is automatically set when the "gelModels" is
created.
This is the method for optim.
Which algorithm should be used to maximize the GEL objective
function. If set to "Wu", which is only for "EL", the Wu
(2005) algorithm is used.
A vector of integers indicating which
"lambda" are restricted to be equal to 0.
The ETXX_lam is used for ETEL and ETHD. In general, it
computes lambda using ET, and returns the value of the objective
function determined by the gelType.
Anatolyev, S. (2005), GMM, GEL, Serial Correlation, and Asymptotic Bias. Econometrica, 73, 983-1002.
Kitamura, Yuichi (1997), Empirical Likelihood Methods With Weakly Dependent Processes. The Annals of Statistics, 25, 2084-2102.
Kitamura, Y. and Otsu, T. and Evdokimov, K. (2013), Robustness, Infinitesimal Neighborhoods and Moment Restrictions. Econometrica, 81, 1185-1201.
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. (2011), GEL Criteria for Moment Condition Models. Econometric Theory, 27(6), 1192--1235.
Wu, C. (2005), Algorithms and R codes for the pseudo empirical likelihood method in survey sampling. Survey Methodology, 31(2), page 239.