Breakdown in Nonlinear Regression

High Breakdown Point Estimation in Regression

In robust regression theory the estimators, which can “resist” contamination of nearly fifty percent of the data, due to the fact that they are highly important in practice, were intensively studied. In this paper we describe three methods with high breakdown point: the least trimmed squares (LTS), the least median of squares (LMS) and their generalization the least weighted squares (LWS) estim...

Inference in Nonlinear Regression

This paper considers inference in a standard nonlinear regression model. We show that the model is non-regular in the sense that test statistics of interest exhibit a discontinuity in their limit distribution as a function of a parameter in the model. The discontinuity occurs when the coe¢ cient of a nonlinear regressor is zero. This paper establishes the asymptotic distributions of the least s...

Nonlinear regression

Breakdown points of t - type regression

Breakdown points of Cauchy regression-scale estimators

The lower bounds for the explosion and implosion breakdown points of the simultaneous Cauchy M-estimator (Cauchy MLE) of the regression and scale parameters are derived. For appropriate tuning constants, the breakdown point attains the maximum possible value.