In this article,we use penalized spline to estimate the hazard function from a set of censored failure time data.A new approach to estimate the amount of smoothing is provided.Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators.Numerical studies and an example are conducted to evaluate the performances of the new procedure.
In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived.
JIN Jiao & CUI HengJian Department of Statistics and Financial Mathematics, School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing 100875, China
For partial linear model Y = Xτβ0 + g0(T) + with unknown β0 ∈ Rd and an unknown smooth function g0, this paper considers the Huber-Dutter estimators of β0, scale σ for the errors and the function g0 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β0 and σ are shown to be asymptotically normal with the rate of convergence n-1/2 and the B-spline Huber-Dutter estimator of g0 achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of β0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator.
