部分线性变系数模型误差方差的估计

半参数模型既含有参数分量, 又含有非参数分量, 在保留非参数模型灵活性的同时又克服了

Efficient estimation of a semiparametric partially linear varying coefficient model

The semiparametric regression models contain both parametric and nonparametric components, and retain the flexibility of nonparametric models while avoiding the curse of dimensionality.To address these models, procedures combined the common methods in the parametric with these in the nonparametric models were developed in recent years.Nevertheless, it brings challenges for our work since the complexity and difficulty of these procedures are more than a single type regression model.Unlike statistical inference for regression coefficients in the literature, this paper considers the problem of variance estimation in partial linear variable coefficient semiparametric models.By using the local constant function coefficient, the semiparametric model can be converted into a high dimensional linear model.Then the variance estimation based on the least square method is constructed, and the asymptotic normality for the resulting estimator is also established.To reduce the mean square error of the least squares estimator, a regularized least squares method named ridge estimator is proposed.Finally, the numerical simulations are conducted to illustrate the finite sample performance of the proposed two estimation methods.