rhoFct {momentfit}

GEL objective functions

Description

Functions that returns the GEL function \rho(g(\theta,x)'\lambda) and its derivatives.

Usage

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 \rho(gmat \lambda) when derive=0, \rho'(gmat \lambda) when derive=1 and \rho''(gmat \lambda) 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.