# rhoFct: GEL objective functions In gmm4: S4 Generalized Method of Moments

## Description

Functions that returns the GEL function ρ(g(θ,x)'λ) and its derivatives.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 rhoET(gmat, lambda, derive = 0, k = 1) rhoETEL(gmat, lambda, derive = 0, k = 1) rhoEL(gmat, lambda, derive = 0, k = 1) rhoEEL(gmat, lambda, derive = 0, k = 1) rhoREEL(gmat, lambda, derive = 0, k = 1) rhoHD(gmat, lambda, derive = 0, k = 1) rhoETHD(gmat, lambda, derive = 0, k = 1) 

## Arguments

 gmat The n \times q matrix of moments lambda The q \times 1 vector of Lagrange multipliers. derive An integer which indicates which derivative to return 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.

## 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.

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