The Asymptotics of the Mahalanobis Depth-Based Theil-Sen Estimators in Multiple Linear Models
نویسندگان
چکیده
In this article, we propose the use of the Mahalanobis depth to construct fully affine equivalent Theil-Sen estimators of parameters in a multiple linear model. Our construction includes the spatial depth-based Theil-Sen estimators as a special case. We exhibit that the efficiency of the proposed estimators relative to the least squares estimators increases with the number of parameters under independent and identically distributed normal errors. We point out that the estimators are robust with a possible maximal breakdown point and possess bounded influences. We show that the estimators are consistent and asymptotic normal for both deterministic and random covariates under suitable conditions. AMS 2000 subject classification: primary 62G05; 62G20.
منابع مشابه
Theil-Sen Estimators in a Multiple Linear Regression Model
In this article, we propose the Theil-Sen estimators of parameters in a multiple linear regression model based on a multivariate median, generalizing the Theil-Sen estimator in a simple linear regression model. The proposed estimator is shown to be robust, consistent and asymptotically normal under mild conditions, and super-efficient when the error distribution is discontinuous. It can be chos...
متن کاملRobust Regression Estimators When There are Tied Values
There is a vast literature on robust regression estimators, the bulk of which assumes that the dependent (outcome) variable is continuous. Evidently, there are no published results on the impact of tied values in terms of the Type I error probability. A minor goal in this paper to comment generally on problems created by tied values when testing the hypothesis of a zero slope. Simulations indic...
متن کاملDifferenced-Based Double Shrinking in Partial Linear Models
Partial linear model is very flexible when the relation between the covariates and responses, either parametric and nonparametric. However, estimation of the regression coefficients is challenging since one must also estimate the nonparametric component simultaneously. As a remedy, the differencing approach, to eliminate the nonparametric component and estimate the regression coefficients, can ...
متن کاملConsistency and Asymptotic Distribution of the Theil-Sen Estimator
In this paper, we obtain the strong consistency and asymptotic distribution of the Theil-Sen estimator in simple linear regression models with arbitrary error distributions. We show that the Theil-Sen estimator is super-efficient when the error distribution is discontinuous and that its asymptotic distribution may or may not be normal when the error distribution is continuous. We give an exampl...
متن کاملارزیابی روند تغییرات پوشش گیاهی مناطق خشک و نیمهخشک (مطالعۀ موردی: منطقۀ حفاظتشدۀ توران)
Introduction Vegetation cover is an important indicator in the arid and semi-arid areas and plays an important role in balancing the ecosystems. Monitoring vegetation cover changes is of great importance because of vegetation effects on the environment. This monitoring provides detailed quantitative and qualitative information. It is therefore important to monitor dynamic changes in vegetatio...
متن کامل