关键词: 半参数回归模型, 固定设计, 渐近分布, Ｂｏｏｔｓｔｒａｐ统计量．

Abstract:

We consider semiparametric regression model under fixed design

y_i = x_iβ + g(t_i) + e_i,i=1,2,…,n.

For the estimators β^_n of β and σ^_n² of σ², defined by using the least squares and usual nonparametric weighted method, we use the resampling method to establish the bootstrap statistic β^_n^* for β^_n and σ^_n^*2 for σ^_n², and then prove that under the given original sample the asymptotic distributions of n^1/2(β^_n^* -β^_n) and n^1/2(σ^_n^*2 -σ^_n^*2) are same as the ones of n^1/2(β^_n-β) and n^1/2(σ^_n²-σ²), respectively.

Key words: Ｓｅｍｉｐａｒａｍｅｔｒｉｃｒｅｇｒｅｓｓｉｏｎ ｍｏｄｅｌ, Ｆｉｘｅｄｄｅｓｉｇｎ, Ａｓｙｍｐｔｏｔｉｃｄｉｓｔｒｉｂｕｔｉｏｎ , Ｂｏｏｔｓｔｒａｐｓｔａｔｉｓｔｉｃ