Variance Estimation in Partially Linear Varying Coefficient Models

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.