BOUNDED INFLUENCE METHODS IN ECONOMETRICS WITH AN APPLICATION TO THE CENSORED REGRESSION MODEL

The Introduction overviews current research on robustness, justifies the particular approach followed, and outlines the results obtained.;Chpt. 3 investigates the robustness of a general class of multi-dimensional tests based on M-estimators. These tests are shown to inherit the efficiency and robustness properties of the estimators on which they are based. In particular, it is shown that a small amount of contamination may have arbitrarily large effects on the level and power of classical tests. An 'admissibility' result is also presented, that provides a justification for using tests based on the optimal bounded-influence estimators discussed in Chpt. 2.;Chpt. 4 considers the problem of estimating Engel curves using household budget data containing a significant fraction of reported zero expenditure. Several assumptions underlying the standard censored regression (or Tobit) model are tested, and the Tobit ML estimator is compared with two alternative types of estimators. The first type are semi-parametric estimators, namely the censored LAD and the symmetrically censored LS estimator. The second type are bounded-influence estimators based on the results of Chpt. 2. ML estimates appear to be very sensitive to extreme observations and are completely unreliable in some cases. Semi-parametric and bounded-influence estimates tend to be close to each other and look more reliable. However, bounded-influence estimates tend to be more precise. Finally, specification tests based on the difference between ML and bounded-influence estimates, and the robust weights provide useful information for identifying sources of model failures, in particular outliers and high leverage points.;Chpt. 2 considers estimation of a multi-dimensional parameter. Hampel's optimality problem for M-estimators with a bounded influence function is generalized to allow for arbitrary choices of the asymptotic efficiency criterion and the norm of the influence function. The method of proof allows further extensions to various cases of practical interest. The linear regression model is used as an illustration, and preliminary results of a set of Monte Carlo experiments are summarized.