Strong consistency of kernel estimator in a semiparametric regression model
share
Estimating the effective dimension reduction (EDR) space, related to the semiparametric regression model introduced by Li sir, is based on the estimation of the covariance matrix Λ of the conditional expectation of the vector of predictors given the response. An estimator Λ_n of Λ based on kernel method was introduced by Zhu and Fang Asymptotics who then derived, under some conditions, the asymptotic distribution of √(n)(Λ_n-Λ), as n→ +∞. In this paper, we obtain, under specified conditions, the almost sure convergence of Λ_n to Λ, as n→ +∞.
READ FULL TEXT