General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

High breakdown-point regression estimators protect against large errors and data con- tamination. Motivated by some { the least trimmed squares and maximum trimmed like- lihood estimators { we propose a general trimmed estimator, which unifies and extends many existing robust procedures. We derive here the consistency and rate of convergence of the proposed general trimmed estimator under mild -mixing conditions and demon- strate its applicability in nonlinear regression, time series, limited dependent variable models, and panel data.consistency;regression;robust estimation;trimming

Trimmed Likelihood-based Estimation in Binary Regression Models

The binary-choice regression models such as probit and logit are typically estimated by the maximum likelihood method.To improve its robustness, various M-estimation based procedures were proposed, which however require bias corrections to achieve consistency and their resistance to outliers is relatively low.On the contrary, traditional high-breakdown point methods such as maximum trimmed likelihood are not applicable since they induce the separation of data and thus non-identification of estimates by trimming observations.We propose a new robust estimator of binary-choice models based on a maximum symmetrically trimmed likelihood estimator.It is proved to be identified and consistent, and additionally, it does not create separation in the space of explanatory variables as the existing maximum trimmed likelihood.We also discuss asymptotic and robust properties of the proposed method and compare all methods by means of Monte Carlo simulations.regression analysis;maximum likelihood;binary-choice regression;robust estimation;trimming

Reweighted Least Trimmed Squares: An Alternative to One-Step Estimators

A new class of robust regression estimators is proposed that forms an alternative to traditional robust one-step estimators and that achieves the √n rate of convergence irrespective of the initial estimator under a wide range of distributional assumptions. The proposed reweighted least trimmed squares (RLTS) estimator employs data-dependent weights determined from an initial robust fit. Just like many existing one- and two-step robust methods, the RLTS estimator preserves robust properties of the initial robust estimate. However contrary to existing methods, the first-order asymptotic behavior of RLTS is independent of the initial estimate even if errors exhibit heteroscedasticity, asymmetry, or serial correlation. Moreover, we derive the asymptotic distribution of RLTS and show that it is asymptotically efficient for normally distributed errors. A simulation study documents benefits of these theoretical properties in finite samples.asymptotic efficiency;breakdown point;least trimmed squares

Efficient Robust Estimation of Regression Models (Revision of DP 2006-08)

This paper introduces a new class of robust regression estimators. The proposed twostep least weighted squares (2S-LWS) estimator employs data-adaptive weights determined from the empirical distribution, quantile, or density functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However contrary to existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions; most importantly, the initial estimator does not need to be pn consistent. Moreover, we prove that 2S-LWS is asymptotically normal under B-mixing conditions and asymptotically efficient if errors are normally distributed. A simulation study documents these theoretical properties in finite samples; in particular, the relative efficiency of 2S-LWS can reach 85–90% in samples of several tens of observations under various distributional models.asymptotic efficiency;breakdown point;least weighted squares

Generalized Methods of Trimmed Moments

High breakdown-point regression estimators protect against large errors and data contamination. We adapt and generalize the concept of trimming used by many of these robust estimators so that it can be employed in the context of the generalized method of moments. The proposed generalized method of trimmed moments (GMTM) offers a globally robust estimation approach (contrary to existing only locally robust estimators) applicable in econometric models identified and estimated using moment conditions. We derive the consistency and asymptotic distribution of GMTM in a general setting, propose a robust test of overidentifying conditions, and demonstrate the application of GMTM in the instrumental variable regression. We also compare the finite-sample performance of GMTM and existing estimators by means of Monte Carlo simulation.asymptotic normality;generalized method of moments;instrumental variables regression;robust estimation;trimming

Semiparametric Robust Estimation of Truncated and Censored Regression Models

Many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares (SCLS) are sensitive to outliers and data contamination as we document. Therefore, we propose a semipara- metric general trimmed estimator (GTE) of truncated and censored regression, which is highly robust and relatively imprecise. To improve its performance, we also propose data-adaptive and one-step trimmed estimators. We derive the robust and asymptotic properties of all proposed estimators and show that the one-step estimators (e.g., one-step SCLS) are as robust as GTE and are asymptotically equivalent to the original estimator (e.g., SCLS). The infinite-sample properties of existing and proposed estimators are studied by means of Monte Carlo simulations.Asymptotic normality;censored regression;one-step estimation;robust esti- mation;trimming;truncated regression

Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models

The binary-choice regression models such as probit and logit are used to describe the effect of explanatory variables on a binary response vari- able. Typically estimated by the maximum likelihood method, estimates are very sensitive to deviations from a model, such as heteroscedastic- ity and data contamination. At the same time, the traditional robust (high-breakdown point) methods such as the maximum trimmed like- lihood are not applicable since, by trimming observations, they induce the separation of data and non-identification of parameter estimates. To provide a robust estimation method for binary-choice regression, we con- sider a maximum symmetrically-trimmed likelihood estimator (MSTLE) and design a parameter-free adaptive procedure for choosing the amount of trimming. The proposed adaptive MSTLE preserves the robust prop- erties of the original MSTLE, significantly improves the infinite-sample behavior of MSTLE, and additionally, ensures asymptotic efficiency of the estimator under no contamination. The results concerning the trim- ming identification, robust properties, and asymptotic distribution of the proposed method are accompanied by simulation experiments and an application documenting the infinite-sample behavior of some existing and the proposed methods.asymptotic efficiency;binary-choice regression;breakdown point;maximum likelihood estimation;robust estimation;trimming

General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)

High breakdown-point regression estimators protect against large errors and data con- tamination. We generalize the concept of trimming used by many of these robust estima- tors, such as the least trimmed squares and maximum trimmed likelihood, and propose a general trimmed estimator, which renders robust estimators applicable far beyond the standard (non)linear regression models. We derive here the consistency and asymptotic distribution of the proposed general trimmed estimator under mild B-mixing conditions and demonstrate its applicability in nonlinear regression and limited dependent variable models.asymptotic normality;regression;robust estimation;trimming

One-Step Robust Estimation of Fixed-Effects Panel Data Models

The panel-data regression models are frequently applied to micro-level data, which often suffer from data contamination, erroneous observations, or unobserved heterogeneity. Despite the adverse effects of outliers on classical estimation methods, there are only a few robust estimation methods available for fixed-effect panel data. Aiming at estimation under weak moment conditions, a new estimation approach based on two different data transformation is proposed. Considering several robust estimation methods applied on the transformed data, we derive the finite-sample, robust, and asymptotic properties of the proposed estimators including their breakdown points and asymptotic distribution. The finite-sample performance of the existing and proposed methods is compared by means of Monte Carlo simulations.breakdown point;fixed effects;panel data;robust estimation

General Trimmed Estimation:Robust Approach to Nonlinear and Limited Dependent Variable Models

High breakdown-point regression estimators protect against large errors and data con- tamination. Motivated by some { the least trimmed squares and maximum trimmed like- lihood estimators { we propose a general trimmed estimator, which unifies and extends many existing robust procedures. We derive here the consistency and rate of convergence of the proposed general trimmed estimator under mild -mixing conditions and demon- strate its applicability in nonlinear regression, time series, limited dependent variable models, and panel data