半参数回归模型中非参数信号的推估——三次样条函数插值法
Deducing and Estimating Nonparametric Signal in Semiparametric Regression Model──Method of Cubic Splines Interpolation
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摘要: 对于半参数回归模型yi= X iTβ+s(ti)+ei,在文献1的基础上考虑其非参数信号s(t)的推估?(t),从而有利于研究非参数信号;接着给出了s(t)与?(t)的偏差大小,从而为推估的准确性提供理论依据;并以实例加以证明。Abstract: This paper considers the semiparametric regression model yi= X iTβ+s(ti)+ei(for i=1,2,...,n). Where si=s(ti) denotes the nonparametric signal of the observation and yi a number relating to the observation at ti, X i∈Rp(n > p), β=(β1,...,βp)T is parameter vector with p denoting the number of parameters, ei denotes the noise and is assumed to be independently N(0,σi2) distributed.
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