Robust inference with GMM estimators

By Elvezio Ronchetti, Fabio Trojani. 2001

167 citations recorded by the source corpus.

The local robustness properties of generalized method of moments (GMM) estimators and of a broad class of GMM based tests are investigated in a unified framework. GMM statistics are shown to have bounded influence if and only if the function defining the orthogonality restrictions imposed on the underlying model is bounded. Since in many applications this function is unbounded, it is useful to have procedures that modify the starting orthogonality conditions in order to obtain a robust version of a GMM estimator or test. We show how this can be obtained when a reference model for the data distribution can be assumed. We develop a flexible algorithm for constructing a robust GMM (RGMM) estimator leading to stable GMM test statistics. The amount of robustness can be controlled by an appropriate tuning constant. We relate by an explicit formula the choice of this constant to the maximal admissible bias on the level or (and) the power of a GMM test and the amount of contamination that one can reasonably assume given some information on the data. Finally, we illustrate the RGMM methodology with some simulations of an application to RGMM testing for conditional heteroscedasticity in a simple linear autoregressive model. In this example we find a significant instability of the size and the power of a classical GMM testing procedure under a non-normal conditional error distribution. On the other side, the RGMM testing procedures can control the size and the power of the test under non-standard conditions while maintaining a satisfactory power under an approximatively normal conditional error distribution.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7b3a3ab184d29f46db595b00b332a55089731d78

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Robust estimates for GARCH models (2008, methodology): “Robust tests for ARCH heteroskedasticity were proposed by van Dijk, Lucas and Franses (1999) and Ronchetti and Trojani (2001).”
Robust Inference for Generalized Linear Models (2001, background): “For example, if q = 1 we have P = 1, diag(P11TP T ) = 1, and • = 0:1145, see Ronchetti and Trojani (2001) .”
Robust Value at Risk Prediction (2007, unknown): “It can be chosen according to an estimator’s efficiency criterion (as in Mancini et al. (2005)) or based on a more inference oriented principle (see Ronchetti and Trojani (2001)).”
Measuring the Sensitivity of Parameter Estimates to Sample Statistics (2014, background): “6 The intuition for this result is that˜g i and˜m i are plug-in estimators for the influence of observation i, a measure of the observation's effect on the value of the estimator (Hampel et al. 1986; Ronchetti and Trojani 2001).”