Strong consistency of kernel estimator in a semiparametric regression model

11/06/2018
by   Emmanuel De Dieu Nkou, et al.
0

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→ +∞.

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