The ordinary least square(OLS)method is commonly used in regression analysis.But in the presence of outlier in the data,its results are unreliable.Hence,the robust regression methods have been suggested for a long tim...The ordinary least square(OLS)method is commonly used in regression analysis.But in the presence of outlier in the data,its results are unreliable.Hence,the robust regression methods have been suggested for a long time as alternatives to the OLS to solve the outliers problem.In the present study,new ratio type estimators of finite population mean are suggested using simple random sampling without replacement(SRSWOR)utilizing the supplementary information in Bowley’s coefficient of skewness with quartiles.For these proposed estimators,we have used the OLS,Huber-M,Mallows GM-estimate,Schweppe GM-estimate,and SIS GM-estimate methods for estimating the population parameters.Theoretically,the mean square error(MSE)equations of various estimators are obtained and compared with the OLS competitor.Simulations for skewed distributions as the Gamma distribution support the results,and an application of real data set containing outliers is considered for illustration.展开更多
For partial linear model Y = X~τβ_0 + g_0(T) + ε with unknown β_0 ∈ R^dand an unknown smooth function g_0, this paper considers the Huber-Dutter estimators of β_0, scaleσ for the errors and the function g_0 res...For partial linear model Y = X~τβ_0 + g_0(T) + ε with unknown β_0 ∈ R^dand an unknown smooth function g_0, this paper considers the Huber-Dutter estimators of β_0, scaleσ for the errors and the function g_0 respectively, in which the smoothing B-spline function isused. Under some regular conditions, it is shown that the Huber-Dutter estimators of β_0 and σ areasymptotically normal with convergence rate n^(-1/2) and the B-spline Huber-Dutter estimator of g_0achieves the optimal convergence rate in nonparametric regression. A simulation study demonstratesthat the Huber-Dutter estimator of β_0 is competitive with its M-estimator without scale parameterand the ordinary least square estimator. An example is presented after the simulation study.展开更多
文摘The ordinary least square(OLS)method is commonly used in regression analysis.But in the presence of outlier in the data,its results are unreliable.Hence,the robust regression methods have been suggested for a long time as alternatives to the OLS to solve the outliers problem.In the present study,new ratio type estimators of finite population mean are suggested using simple random sampling without replacement(SRSWOR)utilizing the supplementary information in Bowley’s coefficient of skewness with quartiles.For these proposed estimators,we have used the OLS,Huber-M,Mallows GM-estimate,Schweppe GM-estimate,and SIS GM-estimate methods for estimating the population parameters.Theoretically,the mean square error(MSE)equations of various estimators are obtained and compared with the OLS competitor.Simulations for skewed distributions as the Gamma distribution support the results,and an application of real data set containing outliers is considered for illustration.
基金Supported by The National Natural Science Foundation of China (No. 10231030 )Beijing Normal University Youth Foundation (No. 104951).
文摘For partial linear model Y = X~τβ_0 + g_0(T) + ε with unknown β_0 ∈ R^dand an unknown smooth function g_0, this paper considers the Huber-Dutter estimators of β_0, scaleσ for the errors and the function g_0 respectively, in which the smoothing B-spline function isused. Under some regular conditions, it is shown that the Huber-Dutter estimators of β_0 and σ areasymptotically normal with convergence rate n^(-1/2) and the B-spline Huber-Dutter estimator of g_0achieves the optimal convergence rate in nonparametric regression. A simulation study demonstratesthat the Huber-Dutter estimator of β_0 is competitive with its M-estimator without scale parameterand the ordinary least square estimator. An example is presented after the simulation study.
