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
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.
