# lambdaAlgo: Algorithms to solve for the Lagrange multiplier In gmm4: S4 Generalized Method of Moments

## Description

The algorithms finds the vector or Lagrange multipliers that maximizes the GEL objective function for a given vector of coefficient θ.

## Usage

 1 2 3 4 5 6 7 8 9 10 11 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())

## Arguments

 gmat The n \times q matrix of moments lambda0 The q \times 1 vector of starting values for the Lagrange multipliers. tol A tolerance level for the stopping rule in the Wu algorithm maxiter The maximum number of iteration in the Wu algorithm gelType 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. rhoFct An optional function that return ρ(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. k 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. method This is the method for optim. algo 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. control A list of control to pass to either optim or nlminb.

## Details

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.

## Value

It returns the vector ρ(gmat λ) when derive=0, ρ'(gmat λ) when derive=1 and ρ''(gmat λ) when derive=2.

## References

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.

gmm4 documentation built on Dec. 6, 2019, 3:01 a.m.