A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of r...A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of leastsquares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the onestep local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.展开更多
We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error t-distribution.The marginal likelihood can also be applied to...We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error t-distribution.The marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.展开更多
This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very m...This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very mild conditions, the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known. The established asymptotic results also hold for two particular local M-estimations: the local least squares and least absolute deviation estimations. However, for general two-stage local M-estimation with continuous and nonlinear ψ-functions, its implementation is time-consuming. To reduce the computational burden, one-step approximations to the two-stage local M-estimators are developed. The one-step estimators are shown to achieve the same efficiency as the fully iterative two-stage local M-estimators, which makes the two-stage local M-estimation more feasible in practice. The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers. In addition, the practical implementation of the proposed estimation is considered in details. Simulations demonstrate the merits of the two-stage local M-estimation, and a real example illustrates the performance of the methodology.展开更多
The paper deals with an analysis of how to use certain measures of location in analysis of salaries. One of the traditional measures of location, the mean should offer typical value of variable, representing all its v...The paper deals with an analysis of how to use certain measures of location in analysis of salaries. One of the traditional measures of location, the mean should offer typical value of variable, representing all its values by the best way. Sometimes, the mean is located in the tail of the distribution and gives a very biased idea about the location of the distribution. In these cases, using different measures of location could be useful. Trimmed mean is described. The trimmed mean refers to a situation where a certain proportion of the largest and smallest observations are removed and the remaining observations are averaged. The construction of some measures of location is based on the analysis of outliers. Outliers are characterized. Then the possibilities of the detection of outliers are analyzed. Computing of one-step M-estimator and modified one-step M-estimator of location is described. A comparison of the trimmed means and M-estimators of location is presented. Finally, the paper focuses on the application of the trimmed mean and M-estimators of location in analysis of salaries. The analysis of salaries of employers of the big Slovak companies in second half of the year 2009 is realized. The data from the census are used in the analysis. The median, 20% trimmed mean and the characteristics, based on the one-step M-estimator of location and modified one step M-estimator, are calculated.展开更多
文摘A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of leastsquares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the onestep local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.
基金The research was partially supported by the National Natural Science Foundation of China(Grant No.10231030)the Excellent Young Teacher Program of the Ministry of Education of China.
文摘We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error t-distribution.The marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.
基金supported by the National Natural Science Foundation of China (Grant No. 10471006)
文摘This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very mild conditions, the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known. The established asymptotic results also hold for two particular local M-estimations: the local least squares and least absolute deviation estimations. However, for general two-stage local M-estimation with continuous and nonlinear ψ-functions, its implementation is time-consuming. To reduce the computational burden, one-step approximations to the two-stage local M-estimators are developed. The one-step estimators are shown to achieve the same efficiency as the fully iterative two-stage local M-estimators, which makes the two-stage local M-estimation more feasible in practice. The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers. In addition, the practical implementation of the proposed estimation is considered in details. Simulations demonstrate the merits of the two-stage local M-estimation, and a real example illustrates the performance of the methodology.
文摘The paper deals with an analysis of how to use certain measures of location in analysis of salaries. One of the traditional measures of location, the mean should offer typical value of variable, representing all its values by the best way. Sometimes, the mean is located in the tail of the distribution and gives a very biased idea about the location of the distribution. In these cases, using different measures of location could be useful. Trimmed mean is described. The trimmed mean refers to a situation where a certain proportion of the largest and smallest observations are removed and the remaining observations are averaged. The construction of some measures of location is based on the analysis of outliers. Outliers are characterized. Then the possibilities of the detection of outliers are analyzed. Computing of one-step M-estimator and modified one-step M-estimator of location is described. A comparison of the trimmed means and M-estimators of location is presented. Finally, the paper focuses on the application of the trimmed mean and M-estimators of location in analysis of salaries. The analysis of salaries of employers of the big Slovak companies in second half of the year 2009 is realized. The data from the census are used in the analysis. The median, 20% trimmed mean and the characteristics, based on the one-step M-estimator of location and modified one step M-estimator, are calculated.
