Abstract: Consider tile partial linear model Y=Xβ+ g(T) + e. Where Y is at risk of being censored from the right, g is an unknown smoothing function on[0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator Σ_n^* ≡(θ^n*)-2 E_n^*(Σ_n^*≡(θ^n*)^-2Ê_n^*) for the asymptotic variance of β_n^*(β_n^*) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for E_n^*, and obtain the convergest rates for E_n^* and the strong uniform convergent rates for ĝ_n^*(g_n^*).

Key words: Partial linear model, Censored data, Kernel method, Asymptotic normality, The law of the iterated logarithm