The convergence rate of estimation for parameter in a semi-parammetric model

We consider semiparametric modelY=X’β+g（T）+e,where （X,T）is random vector onR^p×0,1, β is a p-dimensional unknown parameter, g（·） is an unknown function on0, 1, e is random error with mean 0 and variance σ².And（X,T） and ε are independent each other. We estimate β, σ² by nonparam-etric weight function and least squared method. In this paper, we prove that these estimations of β, σ² have law of the iterated logarithm.