  Estimating the effective dimension reduction (EDR) space, related to the
semiparametric regression model introduced by Li \cite{sir}, is based on the
estimation of the covariance matrix $\Lambda$ of the conditional expectation of
the vector of predictors given the response. An estimator $\widehat{\Lambda}_n$
of $\Lambda $ based on kernel method was introduced by Zhu and Fang
\cite{Asymptotics} who then derived, under some conditions, the asymptotic
distribution of $\sqrt{n}\left(\widehat{\Lambda}_n-\Lambda\right)$, as
$n\rightarrow +\infty$. In this paper, we obtain, under specified conditions,
the almost sure convergence of $\widehat{\Lambda}_n$ to $\Lambda$, as
$n\rightarrow +\infty$.
